x2-12x+52=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-12, and c=52 into the quadratic formula and solve for x.

12±(-12)2-4⋅(1⋅52)2⋅1

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅52)2⋅1

Multiply 52 by 1.

x=12±144-4⋅522⋅1

Multiply -4 by 52.

x=12±144-2082⋅1

Subtract 208 from 144.

x=12±-642⋅1

Rewrite -64 as -1(64).

x=12±-1⋅642⋅1

Rewrite -1(64) as -1⋅64.

x=12±-1⋅642⋅1

Rewrite -1 as i.

x=12±i⋅642⋅1

Rewrite 64 as 82.

x=12±i⋅822⋅1

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

x=12±i⋅82⋅1

Move 8 to the left of i.

x=12±8i2⋅1

x=12±8i2⋅1

Multiply 2 by 1.

x=12±8i2

Simplify 12±8i2.

x=6±4i

x=6±4i

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅52)2⋅1

Multiply 52 by 1.

x=12±144-4⋅522⋅1

Multiply -4 by 52.

x=12±144-2082⋅1

Subtract 208 from 144.

x=12±-642⋅1

Rewrite -64 as -1(64).

x=12±-1⋅642⋅1

Rewrite -1(64) as -1⋅64.

x=12±-1⋅642⋅1

Rewrite -1 as i.

x=12±i⋅642⋅1

Rewrite 64 as 82.

x=12±i⋅822⋅1

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

x=12±i⋅82⋅1

Move 8 to the left of i.

x=12±8i2⋅1

x=12±8i2⋅1

Multiply 2 by 1.

x=12±8i2

Simplify 12±8i2.

x=6±4i

Change the ± to +.

x=6+4i

x=6+4i

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅52)2⋅1

Multiply 52 by 1.

x=12±144-4⋅522⋅1

Multiply -4 by 52.

x=12±144-2082⋅1

Subtract 208 from 144.

x=12±-642⋅1

Rewrite -64 as -1(64).

x=12±-1⋅642⋅1

Rewrite -1(64) as -1⋅64.

x=12±-1⋅642⋅1

Rewrite -1 as i.

x=12±i⋅642⋅1

Rewrite 64 as 82.

x=12±i⋅822⋅1

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

x=12±i⋅82⋅1

Move 8 to the left of i.

x=12±8i2⋅1

x=12±8i2⋅1

Multiply 2 by 1.

x=12±8i2

Simplify 12±8i2.

x=6±4i

Change the ± to -.

x=6-4i

x=6-4i

The final answer is the combination of both solutions.

x=6+4i,6-4i

Solve Using the Square Root Property x^2-12x+52=0