# Solve by Substitution p=q^2+8q+16 , p=-3q^2+6q+436 ,
Substitute for into then solve for .
Replace with in the equation.
Solve the equation for .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Subtract from both sides of the equation.
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.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor.
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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.
Divide each term in by .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
Multiply by by adding the exponents.
Move .
Multiply by .
Move to the left of .
Multiply by .
Multiply by .
Subtract from .
Divide by .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Multiply by .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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.
Set the first factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
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 .
Replace with in the equation.
Simplify .
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
Simplify by adding numbers.
Substitute for into then solve for .
Replace with in the equation.
Simplify .
Simplify each term.
Use the power rule to distribute the exponent.
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 .
Combine and .
Multiply by .
Move the negative in front of the fraction.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Find the common denominator.
Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine fractions.
Combine fractions with similar denominators.
Multiply.
Multiply by .
Multiply by .
Simplify the numerator.
Subtract from .
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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