# Solve using the Square Root Property -2x(x-4)=-16+x -2x(x-4)=-16+x
Simplify -2x(x-4).
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
Move all terms containing x to the left side of the equation.
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+7x+16.
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
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.
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
x=7±1772⋅2
x=7±1772⋅2
Multiply 2 by 2.
x=7±1774
x=7±1774
Simplify the expression to solve for the + portion of the ±.
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
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 expression to solve for the – portion of the ±.
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
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     