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 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

Add 16 and 24.

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 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

Add 16 and 24.

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 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

Add 16 and 24.

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