Solve by Substitution p=q^2+8q+16 , p=-3q^2+6q+436

Math
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Substitute for into then solve for .
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Replace with in the equation.
Solve the equation for .
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Move all terms containing to the left side of the equation.
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Add to both sides of the equation.
Subtract from both sides of the equation.
Add and .
Subtract from .
Move to the left side of the equation by subtracting it from both sides.
Subtract from .
Factor the left side of the equation.
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor.
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Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Remove unnecessary parentheses.
Divide each term by and simplify.
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Divide each term in by .
Simplify .
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
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Move .
Multiply by .
Move to the left of .
Multiply by .
Multiply by .
Subtract from .
Divide by .
Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
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Set the next factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
The final solution is all the values that make true.
Substitute for into then solve for .
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Replace with in the equation.
Simplify .
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Simplify each term.
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Raise to the power of .
Multiply by .
Multiply by .
Simplify by adding numbers.
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Add and .
Add and .
Substitute for into then solve for .
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Replace with in the equation.
Simplify .
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Simplify each term.
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Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
Raise to the power of .
Raise to the power of .
Multiply .
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Combine and .
Multiply by .
Move the negative in front of the fraction.
Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Find the common denominator.
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Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine fractions.
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Combine fractions with similar denominators.
Multiply.
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Multiply by .
Multiply by .
Simplify the numerator.
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Subtract from .
Add and .
The solution to the system is the complete set of ordered pairs that are valid solutions.
Solve by Substitution p=q^2+8q+16 , p=-3q^2+6q+436

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