2x-2+x2-2x+x+9+x+4=42

Combine the opposite terms in 2x-2+x2-2x+x+9+x+4.

Subtract 2x from 2x.

-2+x2+0+x+9+x+4=42

Add -2+x2 and 0.

-2+x2+x+9+x+4=42

-2+x2+x+9+x+4=42

Add -2 and 9.

x2+x+7+x+4=42

Add x and x.

x2+2x+7+4=42

Add 7 and 4.

x2+2x+11=42

x2+2x+11=42

Move 42 to the left side of the equation by subtracting it from both sides.

x2+2x+11-42=0

Subtract 42 from 11.

x2+2x-31=0

x2+2x-31=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=2, and c=-31 into the quadratic formula and solve for x.

-2±22-4⋅(1⋅-31)2⋅1

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(1⋅-31)2⋅1

Multiply -31 by 1.

x=-2±4-4⋅-312⋅1

Multiply -4 by -31.

x=-2±4+1242⋅1

Add 4 and 124.

x=-2±1282⋅1

Rewrite 128 as 82⋅2.

Factor 64 out of 128.

x=-2±64(2)2⋅1

Rewrite 64 as 82.

x=-2±82⋅22⋅1

x=-2±82⋅22⋅1

Pull terms out from under the radical.

x=-2±822⋅1

x=-2±822⋅1

Multiply 2 by 1.

x=-2±822

Simplify -2±822.

x=-1±42

x=-1±42

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(1⋅-31)2⋅1

Multiply -31 by 1.

x=-2±4-4⋅-312⋅1

Multiply -4 by -31.

x=-2±4+1242⋅1

Add 4 and 124.

x=-2±1282⋅1

Rewrite 128 as 82⋅2.

Factor 64 out of 128.

x=-2±64(2)2⋅1

Rewrite 64 as 82.

x=-2±82⋅22⋅1

x=-2±82⋅22⋅1

Pull terms out from under the radical.

x=-2±822⋅1

x=-2±822⋅1

Multiply 2 by 1.

x=-2±822

Simplify -2±822.

x=-1±42

Change the ± to +.

x=-1+42

x=-1+42

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(1⋅-31)2⋅1

Multiply -31 by 1.

x=-2±4-4⋅-312⋅1

Multiply -4 by -31.

x=-2±4+1242⋅1

Add 4 and 124.

x=-2±1282⋅1

Rewrite 128 as 82⋅2.

Factor 64 out of 128.

x=-2±64(2)2⋅1

Rewrite 64 as 82.

x=-2±82⋅22⋅1

x=-2±82⋅22⋅1

Pull terms out from under the radical.

x=-2±822⋅1

x=-2±822⋅1

Multiply 2 by 1.

x=-2±822

Simplify -2±822.

x=-1±42

Change the ± to -.

x=-1-42

x=-1-42

The final answer is the combination of both solutions.

x=-1+42,-1-42

The result can be shown in multiple forms.

Exact Form:

x=-1+42,-1-42

Decimal Form:

x=4.65685424…,-6.65685424…

Solve Using the Square Root Property 2x-2+x^2-2x+x+9+x+4=42