# Solve for x y=x^2+2x-24 y=x2+2x-24
Rewrite the equation as x2+2x-24=y.
x2+2x-24=y
Move y to the left side of the equation by subtracting it from both sides.
x2+2x-24-y=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=2, and c=-24-y into the quadratic formula and solve for x.
-2±22-4⋅(1⋅(-24-y))2⋅1
Simplify.
Simplify the numerator.
Raise 2 to the power of 2.
x=-2±4-4⋅(1⋅(-24-y))2⋅1
Multiply -24-y by 1.
x=-2±4-4⋅(-24-y)2⋅1
Apply the distributive property.
x=-2±4-4⋅-24-4(-y)2⋅1
Multiply -4 by -24.
x=-2±4+96-4(-y)2⋅1
Multiply -1 by -4.
x=-2±4+96+4y2⋅1
x=-2±100+4y2⋅1
Factor 4 out of 100+4y.
Factor 4 out of 100.
x=-2±4⋅25+4y2⋅1
Factor 4 out of 4⋅25+4y.
x=-2±4(25+y)2⋅1
x=-2±4(25+y)2⋅1
Rewrite 4(25+y) as 22(52+y).
Rewrite 4 as 22.
x=-2±22(25+y)2⋅1
Rewrite 25 as 52.
x=-2±22(52+y)2⋅1
x=-2±22(52+y)2⋅1
Pull terms out from under the radical.
x=-2±252+y2⋅1
Raise 5 to the power of 2.
x=-2±225+y2⋅1
x=-2±225+y2⋅1
Multiply 2 by 1.
x=-2±225+y2
Simplify -2±225+y2.
x=-1±25+y
x=-1±25+y
The final answer is the combination of both solutions.
x=-1+25+y
x=-1-25+y
Solve for x y=x^2+2x-24     