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

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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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
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