# Solve Using the Square Root Property -x^2-4x-4x=3

-x2-4x-4x=3
Subtract 4x from -4x.
-x2-8x=3
Move 3 to the left side of the equation by subtracting it from both sides.
-x2-8x-3=0
Factor -1 out of -x2-8x-3.
Factor -1 out of -x2.
-(x2)-8x-3=0
Factor -1 out of -8x.
-(x2)-(8x)-3=0
Rewrite -3 as -1(3).
-(x2)-(8x)-1⋅3=0
Factor -1 out of -(x2)-(8x).
-(x2+8x)-1⋅3=0
Factor -1 out of -(x2+8x)-1(3).
-(x2+8x+3)=0
-(x2+8x+3)=0
Multiply each term in -(x2+8x+3)=0 by -1
Multiply each term in -(x2+8x+3)=0 by -1.
-(x2+8x+3)⋅-1=0⋅-1
Simplify -(x2+8x+3)⋅-1.
Apply the distributive property.
(-x2-(8x)-1⋅3)⋅-1=0⋅-1
Simplify.
Multiply 8 by -1.
(-x2-8x-1⋅3)⋅-1=0⋅-1
Multiply -1 by 3.
(-x2-8x-3)⋅-1=0⋅-1
(-x2-8x-3)⋅-1=0⋅-1
Apply the distributive property.
-x2⋅-1-8x⋅-1-3⋅-1=0⋅-1
Simplify.
Multiply -x2⋅-1.
Multiply -1 by -1.
1×2-8x⋅-1-3⋅-1=0⋅-1
Multiply x2 by 1.
x2-8x⋅-1-3⋅-1=0⋅-1
x2-8x⋅-1-3⋅-1=0⋅-1
Multiply -1 by -8.
x2+8x-3⋅-1=0⋅-1
Multiply -3 by -1.
x2+8x+3=0⋅-1
x2+8x+3=0⋅-1
x2+8x+3=0⋅-1
Multiply 0 by -1.
x2+8x+3=0
x2+8x+3=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=8, and c=3 into the quadratic formula and solve for x.
-8±82-4⋅(1⋅3)2⋅1
Simplify.
Simplify the numerator.
Raise 8 to the power of 2.
x=-8±64-4⋅(1⋅3)2⋅1
Multiply 3 by 1.
x=-8±64-4⋅32⋅1
Multiply -4 by 3.
x=-8±64-122⋅1
Subtract 12 from 64.
x=-8±522⋅1
Rewrite 52 as 22⋅13.
Factor 4 out of 52.
x=-8±4(13)2⋅1
Rewrite 4 as 22.
x=-8±22⋅132⋅1
x=-8±22⋅132⋅1
Pull terms out from under the radical.
x=-8±2132⋅1
x=-8±2132⋅1
Multiply 2 by 1.
x=-8±2132
Simplify -8±2132.
x=-4±13
x=-4±13
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 8 to the power of 2.
x=-8±64-4⋅(1⋅3)2⋅1
Multiply 3 by 1.
x=-8±64-4⋅32⋅1
Multiply -4 by 3.
x=-8±64-122⋅1
Subtract 12 from 64.
x=-8±522⋅1
Rewrite 52 as 22⋅13.
Factor 4 out of 52.
x=-8±4(13)2⋅1
Rewrite 4 as 22.
x=-8±22⋅132⋅1
x=-8±22⋅132⋅1
Pull terms out from under the radical.
x=-8±2132⋅1
x=-8±2132⋅1
Multiply 2 by 1.
x=-8±2132
Simplify -8±2132.
x=-4±13
Change the ± to +.
x=-4+13
x=-4+13
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 8 to the power of 2.
x=-8±64-4⋅(1⋅3)2⋅1
Multiply 3 by 1.
x=-8±64-4⋅32⋅1
Multiply -4 by 3.
x=-8±64-122⋅1
Subtract 12 from 64.
x=-8±522⋅1
Rewrite 52 as 22⋅13.
Factor 4 out of 52.
x=-8±4(13)2⋅1
Rewrite 4 as 22.
x=-8±22⋅132⋅1
x=-8±22⋅132⋅1
Pull terms out from under the radical.
x=-8±2132⋅1
x=-8±2132⋅1
Multiply 2 by 1.
x=-8±2132
Simplify -8±2132.
x=-4±13
Change the ± to -.
x=-4-13
x=-4-13
The final answer is the combination of both solutions.
x=-4+13,-4-13
The result can be shown in multiple forms.
Exact Form:
x=-4+13,-4-13
Decimal Form:
x=-0.39444872…,-7.60555127…
Solve Using the Square Root Property -x^2-4x-4x=3