# Solve Using the Square Root Property x^2+4x+1=0 x2+4x+1=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=4, and c=1 into the quadratic formula and solve for x.
-4±42-4⋅(1⋅1)2⋅1
Simplify.
Simplify the numerator.
Raise 4 to the power of 2.
x=-4±16-4⋅(1⋅1)2⋅1
Multiply 1 by 1.
x=-4±16-4⋅12⋅1
Multiply -4 by 1.
x=-4±16-42⋅1
Subtract 4 from 16.
x=-4±122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=-4±4(3)2⋅1
Rewrite 4 as 22.
x=-4±22⋅32⋅1
x=-4±22⋅32⋅1
Pull terms out from under the radical.
x=-4±232⋅1
x=-4±232⋅1
Multiply 2 by 1.
x=-4±232
Simplify -4±232.
x=-2±3
x=-2±3
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⋅1)2⋅1
Multiply 1 by 1.
x=-4±16-4⋅12⋅1
Multiply -4 by 1.
x=-4±16-42⋅1
Subtract 4 from 16.
x=-4±122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=-4±4(3)2⋅1
Rewrite 4 as 22.
x=-4±22⋅32⋅1
x=-4±22⋅32⋅1
Pull terms out from under the radical.
x=-4±232⋅1
x=-4±232⋅1
Multiply 2 by 1.
x=-4±232
Simplify -4±232.
x=-2±3
Change the ± to +.
x=-2+3
x=-2+3
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⋅1)2⋅1
Multiply 1 by 1.
x=-4±16-4⋅12⋅1
Multiply -4 by 1.
x=-4±16-42⋅1
Subtract 4 from 16.
x=-4±122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
x=-4±4(3)2⋅1
Rewrite 4 as 22.
x=-4±22⋅32⋅1
x=-4±22⋅32⋅1
Pull terms out from under the radical.
x=-4±232⋅1
x=-4±232⋅1
Multiply 2 by 1.
x=-4±232
Simplify -4±232.
x=-2±3
Change the ± to -.
x=-2-3
x=-2-3
The final answer is the combination of both solutions.
x=-2+3,-2-3
The result can be shown in multiple forms.
Exact Form:
x=-2+3,-2-3
Decimal Form:
x=-0.26794919…,-3.73205080…
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