# Solve using the Square Root Property x^2-12x+40=0 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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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     