Algebra Examples

Solve Using the Quadratic Formula x^2-2x-1=0
x2-2x-1=0
Step 1
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Step 2
Substitute the values a=1, b=-2, and c=-1 into the quadratic formula and solve for x.
2±(-2)2-4(1-1)21
Step 3
Simplify.
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Step 3.1
Simplify the numerator.
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Step 3.1.1
Raise -2 to the power of 2.
x=2±4-41-121
Step 3.1.2
Multiply -41-1.
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Step 3.1.2.1
Multiply -4 by 1.
x=2±4-4-121
Step 3.1.2.2
Multiply -4 by -1.
x=2±4+421
x=2±4+421
Step 3.1.3
Add 4 and 4.
x=2±821
Step 3.1.4
Rewrite 8 as 222.
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Step 3.1.4.1
Factor 4 out of 8.
x=2±4(2)21
Step 3.1.4.2
Rewrite 4 as 22.
x=2±22221
x=2±22221
Step 3.1.5
Pull terms out from under the radical.
x=2±2221
x=2±2221
Step 3.2
Multiply 2 by 1.
x=2±222
Step 3.3
Simplify 2±222.
x=1±2
x=1±2
Step 4
The result can be shown in multiple forms.
Exact Form:
x=1±2
Decimal Form:
x=2.41421356,-0.41421356
x2-2x-1=0
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