# Solve Using the Square Root Property x^2-4x=6 x2-4x=6
Move 6 to the left side of the equation by subtracting it from both sides.
x2-4x-6=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-4, and c=-6 into the quadratic formula and solve for x.
4±(-4)2-4⋅(1⋅-6)2⋅1
Simplify.
Simplify the numerator.
Raise -4 to the power of 2.
x=4±16-4⋅(1⋅-6)2⋅1
Multiply -6 by 1.
x=4±16-4⋅-62⋅1
Multiply -4 by -6.
x=4±16+242⋅1
x=4±402⋅1
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
x=4±4(10)2⋅1
Rewrite 4 as 22.
x=4±22⋅102⋅1
x=4±22⋅102⋅1
Pull terms out from under the radical.
x=4±2102⋅1
x=4±2102⋅1
Multiply 2 by 1.
x=4±2102
Simplify 4±2102.
x=2±10
x=2±10
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -4 to the power of 2.
x=4±16-4⋅(1⋅-6)2⋅1
Multiply -6 by 1.
x=4±16-4⋅-62⋅1
Multiply -4 by -6.
x=4±16+242⋅1
x=4±402⋅1
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
x=4±4(10)2⋅1
Rewrite 4 as 22.
x=4±22⋅102⋅1
x=4±22⋅102⋅1
Pull terms out from under the radical.
x=4±2102⋅1
x=4±2102⋅1
Multiply 2 by 1.
x=4±2102
Simplify 4±2102.
x=2±10
Change the ± to +.
x=2+10
x=2+10
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -4 to the power of 2.
x=4±16-4⋅(1⋅-6)2⋅1
Multiply -6 by 1.
x=4±16-4⋅-62⋅1
Multiply -4 by -6.
x=4±16+242⋅1
x=4±402⋅1
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
x=4±4(10)2⋅1
Rewrite 4 as 22.
x=4±22⋅102⋅1
x=4±22⋅102⋅1
Pull terms out from under the radical.
x=4±2102⋅1
x=4±2102⋅1
Multiply 2 by 1.
x=4±2102
Simplify 4±2102.
x=2±10
Change the ± to -.
x=2-10
x=2-10
The final answer is the combination of both solutions.
x=2+10,2-10
The result can be shown in multiple forms.
Exact Form:
x=2+10,2-10
Decimal Form:
x=5.16227766…,-1.16227766…
Solve Using the Square Root Property x^2-4x=6     