# Solve Using the Square Root Property x^2-6x+4=-8x-7x^2

x2-6x+4=-8x-7×2
Move all terms containing x to the left side of the equation.
Add 8x to both sides of the equation.
x2-6x+4+8x=-7×2
Add 7×2 to both sides of the equation.
x2-6x+4+8x+7×2=0
8×2-6x+4+8x=0
8×2+2x+4=0
8×2+2x+4=0
Factor 2 out of 8×2+2x+4.
Factor 2 out of 8×2.
2(4×2)+2x+4=0
Factor 2 out of 2x.
2(4×2)+2(x)+4=0
Factor 2 out of 4.
2(4×2)+2x+2⋅2=0
Factor 2 out of 2(4×2)+2x.
2(4×2+x)+2⋅2=0
Factor 2 out of 2(4×2+x)+2⋅2.
2(4×2+x+2)=0
2(4×2+x+2)=0
Divide each term by 2 and simplify.
Divide each term in 2(4×2+x+2)=0 by 2.
2(4×2+x+2)2=02
Cancel the common factor of 2.
Cancel the common factor.
2(4×2+x+2)2=02
Divide 4×2+x+2 by 1.
4×2+x+2=02
4×2+x+2=02
Divide 0 by 2.
4×2+x+2=0
4×2+x+2=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=1, and c=2 into the quadratic formula and solve for x.
-1±12-4⋅(4⋅2)2⋅4
Simplify.
Simplify the numerator.
One to any power is one.
x=-1±1-4⋅(4⋅2)2⋅4
Multiply 4 by 2.
x=-1±1-4⋅82⋅4
Multiply -4 by 8.
x=-1±1-322⋅4
Subtract 32 from 1.
x=-1±-312⋅4
Rewrite -31 as -1(31).
x=-1±-1⋅312⋅4
Rewrite -1(31) as -1⋅31.
x=-1±-1⋅312⋅4
Rewrite -1 as i.
x=-1±i312⋅4
x=-1±i312⋅4
Multiply 2 by 4.
x=-1±i318
x=-1±i318
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
One to any power is one.
x=-1±1-4⋅(4⋅2)2⋅4
Multiply 4 by 2.
x=-1±1-4⋅82⋅4
Multiply -4 by 8.
x=-1±1-322⋅4
Subtract 32 from 1.
x=-1±-312⋅4
Rewrite -31 as -1(31).
x=-1±-1⋅312⋅4
Rewrite -1(31) as -1⋅31.
x=-1±-1⋅312⋅4
Rewrite -1 as i.
x=-1±i312⋅4
x=-1±i312⋅4
Multiply 2 by 4.
x=-1±i318
Change the ± to +.
x=-1+i318
Rewrite -1 as -1(1).
x=-1⋅1+i318
Factor -1 out of i31.
x=-1⋅1-(-i31)8
Factor -1 out of -1(1)-(-i31).
x=-1(1-i31)8
Move the negative in front of the fraction.
x=-1-i318
x=-1-i318
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
One to any power is one.
x=-1±1-4⋅(4⋅2)2⋅4
Multiply 4 by 2.
x=-1±1-4⋅82⋅4
Multiply -4 by 8.
x=-1±1-322⋅4
Subtract 32 from 1.
x=-1±-312⋅4
Rewrite -31 as -1(31).
x=-1±-1⋅312⋅4
Rewrite -1(31) as -1⋅31.
x=-1±-1⋅312⋅4
Rewrite -1 as i.
x=-1±i312⋅4
x=-1±i312⋅4
Multiply 2 by 4.
x=-1±i318
Change the ± to -.
x=-1-i318
Rewrite -1 as -1(1).
x=-1⋅1-i318
Factor -1 out of -i31.
x=-1⋅1-(i31)8
Factor -1 out of -1(1)-(i31).
x=-1(1+i31)8
Move the negative in front of the fraction.
x=-1+i318
x=-1+i318
The final answer is the combination of both solutions.
x=-1-i318,-1+i318
Solve Using the Square Root Property x^2-6x+4=-8x-7x^2