# Solve by Substitution y=x^2+12x+30 , 8x-y=10 ,
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Subtract from .
Solve for in the first equation.
Move all terms to the left side of the equation and simplify.
Subtract from both sides of the equation.
Subtract from .
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
Multiply by .
Simplify .
Move the negative one from the denominator of .
Rewrite as .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
Multiply by .
Simplify .
Move the negative one from the denominator of .
Rewrite as .
Change the to .
Apply the distributive property.
Multiply by .
Multiply by .
Simplify the expression to solve for the portion of the .
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
Multiply by .
Simplify .
Move the negative one from the denominator of .
Rewrite as .
Change the to .
Apply the distributive property.
Multiply by .
Multiply by .
The final answer is the combination of both solutions.
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Rewrite as .
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.
Multiply by .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Multiply by .
Subtract from .
Apply the distributive property.
Multiply by .
Multiply by .
Simplify by adding terms.
Subtract from .
Subtract from .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Rewrite as .
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.
Multiply by .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Multiply by .
Subtract from .
Subtract from .
Apply the distributive property.
Multiply by .
Multiply by .
Simplify by adding terms.
Subtract from .     