-2x(x-4)=-16+x

Apply the distributive property.

-2x⋅x-2x⋅-4=-16+x

Multiply x by x by adding the exponents.

Move x.

-2(x⋅x)-2x⋅-4=-16+x

Multiply x by x.

-2×2-2x⋅-4=-16+x

-2×2-2x⋅-4=-16+x

Multiply -4 by -2.

-2×2+8x=-16+x

-2×2+8x=-16+x

Subtract x from both sides of the equation.

-2×2+8x-x=-16

Subtract x from 8x.

-2×2+7x=-16

-2×2+7x=-16

Move 16 to the left side of the equation by adding it to both sides.

-2×2+7x+16=0

Factor -1 out of -2×2.

-(2×2)+7x+16=0

Factor -1 out of 7x.

-(2×2)-(-7x)+16=0

Rewrite 16 as -1(-16).

-(2×2)-(-7x)-1⋅-16=0

Factor -1 out of -(2×2)-(-7x).

-(2×2-7x)-1⋅-16=0

Factor -1 out of -(2×2-7x)-1(-16).

-(2×2-7x-16)=0

-(2×2-7x-16)=0

Multiply each term in -(2×2-7x-16)=0 by -1.

-(2×2-7x-16)⋅-1=0⋅-1

Simplify -(2×2-7x-16)⋅-1.

Apply the distributive property.

(-(2×2)-(-7x)–16)⋅-1=0⋅-1

Simplify.

Multiply 2 by -1.

(-2×2-(-7x)–16)⋅-1=0⋅-1

Multiply -7 by -1.

(-2×2+7x–16)⋅-1=0⋅-1

Multiply -1 by -16.

(-2×2+7x+16)⋅-1=0⋅-1

(-2×2+7x+16)⋅-1=0⋅-1

Apply the distributive property.

-2×2⋅-1+7x⋅-1+16⋅-1=0⋅-1

Simplify.

Multiply -1 by -2.

2×2+7x⋅-1+16⋅-1=0⋅-1

Multiply -1 by 7.

2×2-7x+16⋅-1=0⋅-1

Multiply 16 by -1.

2×2-7x-16=0⋅-1

2×2-7x-16=0⋅-1

2×2-7x-16=0⋅-1

Multiply 0 by -1.

2×2-7x-16=0

2×2-7x-16=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=2, b=-7, and c=-16 into the quadratic formula and solve for x.

7±(-7)2-4⋅(2⋅-16)2⋅2

Simplify the numerator.

Raise -7 to the power of 2.

x=7±49-4⋅(2⋅-16)2⋅2

Multiply 2 by -16.

x=7±49-4⋅-322⋅2

Multiply -4 by -32.

x=7±49+1282⋅2

Add 49 and 128.

x=7±1772⋅2

x=7±1772⋅2

Multiply 2 by 2.

x=7±1774

x=7±1774

Simplify the numerator.

Raise -7 to the power of 2.

x=7±49-4⋅(2⋅-16)2⋅2

Multiply 2 by -16.

x=7±49-4⋅-322⋅2

Multiply -4 by -32.

x=7±49+1282⋅2

Add 49 and 128.

x=7±1772⋅2

x=7±1772⋅2

Multiply 2 by 2.

x=7±1774

Change the ± to +.

x=7+1774

x=7+1774

Simplify the numerator.

Raise -7 to the power of 2.

x=7±49-4⋅(2⋅-16)2⋅2

Multiply 2 by -16.

x=7±49-4⋅-322⋅2

Multiply -4 by -32.

x=7±49+1282⋅2

Add 49 and 128.

x=7±1772⋅2

x=7±1772⋅2

Multiply 2 by 2.

x=7±1774

Change the ± to -.

x=7-1774

x=7-1774

The final answer is the combination of both solutions.

x=7+1774,7-1774

The result can be shown in multiple forms.

Exact Form:

x=7+1774,7-1774

Decimal Form:

x=5.07603367…,-1.57603367…

Solve using the Square Root Property -2x(x-4)=-16+x