# Solve using the Square Root Property x^2=6x-25

x2=6x-25
Subtract 6x from both sides of the equation.
x2-6x=-25
Move 25 to the left side of the equation by adding it to both sides.
x2-6x+25=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-6, and c=25 into the quadratic formula and solve for x.
6±(-6)2-4⋅(1⋅25)2⋅1
Simplify.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅25)2⋅1
Multiply 25 by 1.
x=6±36-4⋅252⋅1
Multiply -4 by 25.
x=6±36-1002⋅1
Subtract 100 from 36.
x=6±-642⋅1
Rewrite -64 as -1(64).
x=6±-1⋅642⋅1
Rewrite -1(64) as -1⋅64.
x=6±-1⋅642⋅1
Rewrite -1 as i.
x=6±i⋅642⋅1
Rewrite 64 as 82.
x=6±i⋅822⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=6±i⋅82⋅1
Move 8 to the left of i.
x=6±8i2⋅1
x=6±8i2⋅1
Multiply 2 by 1.
x=6±8i2
Simplify 6±8i2.
x=3±4i
x=3±4i
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅25)2⋅1
Multiply 25 by 1.
x=6±36-4⋅252⋅1
Multiply -4 by 25.
x=6±36-1002⋅1
Subtract 100 from 36.
x=6±-642⋅1
Rewrite -64 as -1(64).
x=6±-1⋅642⋅1
Rewrite -1(64) as -1⋅64.
x=6±-1⋅642⋅1
Rewrite -1 as i.
x=6±i⋅642⋅1
Rewrite 64 as 82.
x=6±i⋅822⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=6±i⋅82⋅1
Move 8 to the left of i.
x=6±8i2⋅1
x=6±8i2⋅1
Multiply 2 by 1.
x=6±8i2
Simplify 6±8i2.
x=3±4i
Change the ± to +.
x=3+4i
x=3+4i
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅25)2⋅1
Multiply 25 by 1.
x=6±36-4⋅252⋅1
Multiply -4 by 25.
x=6±36-1002⋅1
Subtract 100 from 36.
x=6±-642⋅1
Rewrite -64 as -1(64).
x=6±-1⋅642⋅1
Rewrite -1(64) as -1⋅64.
x=6±-1⋅642⋅1
Rewrite -1 as i.
x=6±i⋅642⋅1
Rewrite 64 as 82.
x=6±i⋅822⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=6±i⋅82⋅1
Move 8 to the left of i.
x=6±8i2⋅1
x=6±8i2⋅1
Multiply 2 by 1.
x=6±8i2
Simplify 6±8i2.
x=3±4i
Change the ± to -.
x=3-4i
x=3-4i
The final answer is the combination of both solutions.
x=3+4i,3-4i
Solve using the Square Root Property x^2=6x-25