x2-12x+40=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-12, and c=40 into the quadratic formula and solve for x.

12±(-12)2-4⋅(1⋅40)2⋅1

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅40)2⋅1

Multiply 40 by 1.

x=12±144-4⋅402⋅1

Multiply -4 by 40.

x=12±144-1602⋅1

Subtract 160 from 144.

x=12±-162⋅1

Rewrite -16 as -1(16).

x=12±-1⋅162⋅1

Rewrite -1(16) as -1⋅16.

x=12±-1⋅162⋅1

Rewrite -1 as i.

x=12±i⋅162⋅1

Rewrite 16 as 42.

x=12±i⋅422⋅1

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

x=12±i⋅42⋅1

Move 4 to the left of i.

x=12±4i2⋅1

x=12±4i2⋅1

Multiply 2 by 1.

x=12±4i2

Simplify 12±4i2.

x=6±2i

x=6±2i

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅40)2⋅1

Multiply 40 by 1.

x=12±144-4⋅402⋅1

Multiply -4 by 40.

x=12±144-1602⋅1

Subtract 160 from 144.

x=12±-162⋅1

Rewrite -16 as -1(16).

x=12±-1⋅162⋅1

Rewrite -1(16) as -1⋅16.

x=12±-1⋅162⋅1

Rewrite -1 as i.

x=12±i⋅162⋅1

Rewrite 16 as 42.

x=12±i⋅422⋅1

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

x=12±i⋅42⋅1

Move 4 to the left of i.

x=12±4i2⋅1

x=12±4i2⋅1

Multiply 2 by 1.

x=12±4i2

Simplify 12±4i2.

x=6±2i

Change the ± to +.

x=6+2i

x=6+2i

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅40)2⋅1

Multiply 40 by 1.

x=12±144-4⋅402⋅1

Multiply -4 by 40.

x=12±144-1602⋅1

Subtract 160 from 144.

x=12±-162⋅1

Rewrite -16 as -1(16).

x=12±-1⋅162⋅1

Rewrite -1(16) as -1⋅16.

x=12±-1⋅162⋅1

Rewrite -1 as i.

x=12±i⋅162⋅1

Rewrite 16 as 42.

x=12±i⋅422⋅1

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

x=12±i⋅42⋅1

Move 4 to the left of i.

x=12±4i2⋅1

x=12±4i2⋅1

Multiply 2 by 1.

x=12±4i2

Simplify 12±4i2.

x=6±2i

Change the ± to -.

x=6-2i

x=6-2i

The final answer is the combination of both solutions.

x=6+2i,6-2i

Solve using the Square Root Property x^2-12x+40=0