x2=6x-25

Subtract 6x from both sides of the equation.

x2-6x=-25

Move 25 to the left side of the equation by adding it to both sides.

x2-6x+25=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-6, and c=25 into the quadratic formula and solve for x.

6±(-6)2-4⋅(1⋅25)2⋅1

Simplify the numerator.

Raise -6 to the power of 2.

x=6±36-4⋅(1⋅25)2⋅1

Multiply 25 by 1.

x=6±36-4⋅252⋅1

Multiply -4 by 25.

x=6±36-1002⋅1

Subtract 100 from 36.

x=6±-642⋅1

Rewrite -64 as -1(64).

x=6±-1⋅642⋅1

Rewrite -1(64) as -1⋅64.

x=6±-1⋅642⋅1

Rewrite -1 as i.

x=6±i⋅642⋅1

Rewrite 64 as 82.

x=6±i⋅822⋅1

Pull terms out from under the radical, assuming positive real numbers.

x=6±i⋅82⋅1

Move 8 to the left of i.

x=6±8i2⋅1

x=6±8i2⋅1

Multiply 2 by 1.

x=6±8i2

Simplify 6±8i2.

x=3±4i

x=3±4i

Simplify the numerator.

Raise -6 to the power of 2.

x=6±36-4⋅(1⋅25)2⋅1

Multiply 25 by 1.

x=6±36-4⋅252⋅1

Multiply -4 by 25.

x=6±36-1002⋅1

Subtract 100 from 36.

x=6±-642⋅1

Rewrite -64 as -1(64).

x=6±-1⋅642⋅1

Rewrite -1(64) as -1⋅64.

x=6±-1⋅642⋅1

Rewrite -1 as i.

x=6±i⋅642⋅1

Rewrite 64 as 82.

x=6±i⋅822⋅1

Pull terms out from under the radical, assuming positive real numbers.

x=6±i⋅82⋅1

Move 8 to the left of i.

x=6±8i2⋅1

x=6±8i2⋅1

Multiply 2 by 1.

x=6±8i2

Simplify 6±8i2.

x=3±4i

Change the ± to +.

x=3+4i

x=3+4i

Simplify the numerator.

Raise -6 to the power of 2.

x=6±36-4⋅(1⋅25)2⋅1

Multiply 25 by 1.

x=6±36-4⋅252⋅1

Multiply -4 by 25.

x=6±36-1002⋅1

Subtract 100 from 36.

x=6±-642⋅1

Rewrite -64 as -1(64).

x=6±-1⋅642⋅1

Rewrite -1(64) as -1⋅64.

x=6±-1⋅642⋅1

Rewrite -1 as i.

x=6±i⋅642⋅1

Rewrite 64 as 82.

x=6±i⋅822⋅1

Pull terms out from under the radical, assuming positive real numbers.

x=6±i⋅82⋅1

Move 8 to the left of i.

x=6±8i2⋅1

x=6±8i2⋅1

Multiply 2 by 1.

x=6±8i2

Simplify 6±8i2.

x=3±4i

Change the ± to -.

x=3-4i

x=3-4i

The final answer is the combination of both solutions.

x=3+4i,3-4i

Solve using the Square Root Property x^2=6x-25