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 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

Add 4 and 96.

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