Solve Using the Square Root Property 2x-2+x^2-2x+x+9+x+4=42

Math
2x-2+x2-2x+x+9+x+4=42
Simplify 2x-2+x2-2x+x+9+x+4.
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Combine the opposite terms in 2x-2+x2-2x+x+9+x+4.
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Subtract 2x from 2x.
-2+x2+0+x+9+x+4=42
Add -2+x2 and 0.
-2+x2+x+9+x+4=42
-2+x2+x+9+x+4=42
Add -2 and 9.
x2+x+7+x+4=42
Add x and x.
x2+2x+7+4=42
Add 7 and 4.
x2+2x+11=42
x2+2x+11=42
Move all terms to the left side of the equation and simplify.
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Move 42 to the left side of the equation by subtracting it from both sides.
x2+2x+11-42=0
Subtract 42 from 11.
x2+2x-31=0
x2+2x-31=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=2, and c=-31 into the quadratic formula and solve for x.
-2±22-4⋅(1⋅-31)2⋅1
Simplify.
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Simplify the numerator.
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Raise 2 to the power of 2.
x=-2±4-4⋅(1⋅-31)2⋅1
Multiply -31 by 1.
x=-2±4-4⋅-312⋅1
Multiply -4 by -31.
x=-2±4+1242⋅1
Add 4 and 124.
x=-2±1282⋅1
Rewrite 128 as 82⋅2.
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Factor 64 out of 128.
x=-2±64(2)2⋅1
Rewrite 64 as 82.
x=-2±82⋅22⋅1
x=-2±82⋅22⋅1
Pull terms out from under the radical.
x=-2±822⋅1
x=-2±822⋅1
Multiply 2 by 1.
x=-2±822
Simplify -2±822.
x=-1±42
x=-1±42
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise 2 to the power of 2.
x=-2±4-4⋅(1⋅-31)2⋅1
Multiply -31 by 1.
x=-2±4-4⋅-312⋅1
Multiply -4 by -31.
x=-2±4+1242⋅1
Add 4 and 124.
x=-2±1282⋅1
Rewrite 128 as 82⋅2.
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Factor 64 out of 128.
x=-2±64(2)2⋅1
Rewrite 64 as 82.
x=-2±82⋅22⋅1
x=-2±82⋅22⋅1
Pull terms out from under the radical.
x=-2±822⋅1
x=-2±822⋅1
Multiply 2 by 1.
x=-2±822
Simplify -2±822.
x=-1±42
Change the ± to +.
x=-1+42
x=-1+42
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise 2 to the power of 2.
x=-2±4-4⋅(1⋅-31)2⋅1
Multiply -31 by 1.
x=-2±4-4⋅-312⋅1
Multiply -4 by -31.
x=-2±4+1242⋅1
Add 4 and 124.
x=-2±1282⋅1
Rewrite 128 as 82⋅2.
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Factor 64 out of 128.
x=-2±64(2)2⋅1
Rewrite 64 as 82.
x=-2±82⋅22⋅1
x=-2±82⋅22⋅1
Pull terms out from under the radical.
x=-2±822⋅1
x=-2±822⋅1
Multiply 2 by 1.
x=-2±822
Simplify -2±822.
x=-1±42
Change the ± to -.
x=-1-42
x=-1-42
The final answer is the combination of both solutions.
x=-1+42,-1-42
The result can be shown in multiple forms.
Exact Form:
x=-1+42,-1-42
Decimal Form:
x=4.65685424…,-6.65685424…
Solve Using the Square Root Property 2x-2+x^2-2x+x+9+x+4=42

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