x2-12x+72=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-12, and c=72 into the quadratic formula and solve for x.

12±(-12)2-4⋅(1⋅72)2⋅1

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅72)2⋅1

Multiply 72 by 1.

x=12±144-4⋅722⋅1

Multiply -4 by 72.

x=12±144-2882⋅1

Subtract 288 from 144.

x=12±-1442⋅1

Rewrite -144 as -1(144).

x=12±-1⋅1442⋅1

Rewrite -1(144) as -1⋅144.

x=12±-1⋅1442⋅1

Rewrite -1 as i.

x=12±i⋅1442⋅1

Rewrite 144 as 122.

x=12±i⋅1222⋅1

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

x=12±i⋅122⋅1

Move 12 to the left of i.

x=12±12i2⋅1

x=12±12i2⋅1

Multiply 2 by 1.

x=12±12i2

Simplify 12±12i2.

x=6±6i

x=6±6i

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅72)2⋅1

Multiply 72 by 1.

x=12±144-4⋅722⋅1

Multiply -4 by 72.

x=12±144-2882⋅1

Subtract 288 from 144.

x=12±-1442⋅1

Rewrite -144 as -1(144).

x=12±-1⋅1442⋅1

Rewrite -1(144) as -1⋅144.

x=12±-1⋅1442⋅1

Rewrite -1 as i.

x=12±i⋅1442⋅1

Rewrite 144 as 122.

x=12±i⋅1222⋅1

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

x=12±i⋅122⋅1

Move 12 to the left of i.

x=12±12i2⋅1

x=12±12i2⋅1

Multiply 2 by 1.

x=12±12i2

Simplify 12±12i2.

x=6±6i

Change the ± to +.

x=6+6i

x=6+6i

Simplify the numerator.

Raise -12 to the power of 2.

x=12±144-4⋅(1⋅72)2⋅1

Multiply 72 by 1.

x=12±144-4⋅722⋅1

Multiply -4 by 72.

x=12±144-2882⋅1

Subtract 288 from 144.

x=12±-1442⋅1

Rewrite -144 as -1(144).

x=12±-1⋅1442⋅1

Rewrite -1(144) as -1⋅144.

x=12±-1⋅1442⋅1

Rewrite -1 as i.

x=12±i⋅1442⋅1

Rewrite 144 as 122.

x=12±i⋅1222⋅1

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

x=12±i⋅122⋅1

Move 12 to the left of i.

x=12±12i2⋅1

x=12±12i2⋅1

Multiply 2 by 1.

x=12±12i2

Simplify 12±12i2.

x=6±6i

Change the ± to -.

x=6-6i

x=6-6i

The final answer is the combination of both solutions.

x=6+6i,6-6i

Solve Using the Square Root Property x^2-12x+72=0