x2=6x-10

Subtract 6x from both sides of the equation.

x2-6x=-10

Move 10 to the left side of the equation by adding it to both sides.

x2-6x+10=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-6, and c=10 into the quadratic formula and solve for x.

6±(-6)2-4⋅(1⋅10)2⋅1

Simplify the numerator.

Raise -6 to the power of 2.

x=6±36-4⋅(1⋅10)2⋅1

Multiply 10 by 1.

x=6±36-4⋅102⋅1

Multiply -4 by 10.

x=6±36-402⋅1

Subtract 40 from 36.

x=6±-42⋅1

Rewrite -4 as -1(4).

x=6±-1⋅42⋅1

Rewrite -1(4) as -1⋅4.

x=6±-1⋅42⋅1

Rewrite -1 as i.

x=6±i⋅42⋅1

Rewrite 4 as 22.

x=6±i⋅222⋅1

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

x=6±i⋅22⋅1

Move 2 to the left of i.

x=6±2i2⋅1

x=6±2i2⋅1

Multiply 2 by 1.

x=6±2i2

Simplify 6±2i2.

x=3±i

x=3±i

Simplify the numerator.

Raise -6 to the power of 2.

x=6±36-4⋅(1⋅10)2⋅1

Multiply 10 by 1.

x=6±36-4⋅102⋅1

Multiply -4 by 10.

x=6±36-402⋅1

Subtract 40 from 36.

x=6±-42⋅1

Rewrite -4 as -1(4).

x=6±-1⋅42⋅1

Rewrite -1(4) as -1⋅4.

x=6±-1⋅42⋅1

Rewrite -1 as i.

x=6±i⋅42⋅1

Rewrite 4 as 22.

x=6±i⋅222⋅1

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

x=6±i⋅22⋅1

Move 2 to the left of i.

x=6±2i2⋅1

x=6±2i2⋅1

Multiply 2 by 1.

x=6±2i2

Simplify 6±2i2.

x=3±i

Change the ± to +.

x=3+i

x=3+i

Simplify the numerator.

Raise -6 to the power of 2.

x=6±36-4⋅(1⋅10)2⋅1

Multiply 10 by 1.

x=6±36-4⋅102⋅1

Multiply -4 by 10.

x=6±36-402⋅1

Subtract 40 from 36.

x=6±-42⋅1

Rewrite -4 as -1(4).

x=6±-1⋅42⋅1

Rewrite -1(4) as -1⋅4.

x=6±-1⋅42⋅1

Rewrite -1 as i.

x=6±i⋅42⋅1

Rewrite 4 as 22.

x=6±i⋅222⋅1

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

x=6±i⋅22⋅1

Move 2 to the left of i.

x=6±2i2⋅1

x=6±2i2⋅1

Multiply 2 by 1.

x=6±2i2

Simplify 6±2i2.

x=3±i

Change the ± to -.

x=3-i

x=3-i

The final answer is the combination of both solutions.

x=3+i,3-i

Solve Using the Square Root Property x^2=6x-10