# Solve Using the Square Root Property 2x^2-2x-1=0 2×2-2x-1=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=-2, and c=-1 into the quadratic formula and solve for x.
2±(-2)2-4⋅(2⋅-1)2⋅2
Simplify.
Simplify the numerator.
Raise -2 to the power of 2.
x=2±4-4⋅(2⋅-1)2⋅2
Multiply 2 by -1.
x=2±4-4⋅-22⋅2
Multiply -4 by -2.
x=2±4+82⋅2
Add 4 and 8.
x=2±122⋅2
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=2±4(3)2⋅2
Rewrite 4 as 22.
x=2±22⋅32⋅2
x=2±22⋅32⋅2
Pull terms out from under the radical.
x=2±232⋅2
x=2±232⋅2
Multiply 2 by 2.
x=2±234
Simplify 2±234.
x=1±32
x=1±32
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -2 to the power of 2.
x=2±4-4⋅(2⋅-1)2⋅2
Multiply 2 by -1.
x=2±4-4⋅-22⋅2
Multiply -4 by -2.
x=2±4+82⋅2
Add 4 and 8.
x=2±122⋅2
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=2±4(3)2⋅2
Rewrite 4 as 22.
x=2±22⋅32⋅2
x=2±22⋅32⋅2
Pull terms out from under the radical.
x=2±232⋅2
x=2±232⋅2
Multiply 2 by 2.
x=2±234
Simplify 2±234.
x=1±32
Change the ± to +.
x=1+32
x=1+32
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -2 to the power of 2.
x=2±4-4⋅(2⋅-1)2⋅2
Multiply 2 by -1.
x=2±4-4⋅-22⋅2
Multiply -4 by -2.
x=2±4+82⋅2
Add 4 and 8.
x=2±122⋅2
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=2±4(3)2⋅2
Rewrite 4 as 22.
x=2±22⋅32⋅2
x=2±22⋅32⋅2
Pull terms out from under the radical.
x=2±232⋅2
x=2±232⋅2
Multiply 2 by 2.
x=2±234
Simplify 2±234.
x=1±32
Change the ± to -.
x=1-32
x=1-32
The final answer is the combination of both solutions.
x=1+32,1-32
The result can be shown in multiple forms.
Exact Form:
x=1+32,1-32
Decimal Form:
x=1.36602540…,-0.36602540…
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