x2-6x+4=-8x-7×2

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

Add x2 and 7×2.

8×2-6x+4+8x=0

Add -6x and 8x.

8×2+2x+4=0

8×2+2x+4=0

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 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 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 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 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