Solve Using the Square Root Property 8x=4x^2-1

Math
8x=4×2-1
Subtract 4×2 from both sides of the equation.
8x-4×2=-1
Move 1 to the left side of the equation by adding it to both sides.
8x-4×2+1=0
Factor -1 out of 8x-4×2+1.
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Reorder 8x and -4×2.
-4×2+8x+1=0
Factor -1 out of -4×2.
-(4×2)+8x+1=0
Factor -1 out of 8x.
-(4×2)-(-8x)+1=0
Rewrite 1 as -1(-1).
-(4×2)-(-8x)-1⋅-1=0
Factor -1 out of -(4×2)-(-8x).
-(4×2-8x)-1⋅-1=0
Factor -1 out of -(4×2-8x)-1(-1).
-(4×2-8x-1)=0
-(4×2-8x-1)=0
Multiply each term in -(4×2-8x-1)=0 by -1
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Multiply each term in -(4×2-8x-1)=0 by -1.
-(4×2-8x-1)⋅-1=0⋅-1
Simplify -(4×2-8x-1)⋅-1.
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Apply the distributive property.
(-(4×2)-(-8x)–1)⋅-1=0⋅-1
Simplify.
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Multiply 4 by -1.
(-4×2-(-8x)–1)⋅-1=0⋅-1
Multiply -8 by -1.
(-4×2+8x–1)⋅-1=0⋅-1
Multiply -1 by -1.
(-4×2+8x+1)⋅-1=0⋅-1
(-4×2+8x+1)⋅-1=0⋅-1
Apply the distributive property.
-4×2⋅-1+8x⋅-1+1⋅-1=0⋅-1
Simplify.
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Multiply -1 by -4.
4×2+8x⋅-1+1⋅-1=0⋅-1
Multiply -1 by 8.
4×2-8x+1⋅-1=0⋅-1
Multiply -1 by 1.
4×2-8x-1=0⋅-1
4×2-8x-1=0⋅-1
4×2-8x-1=0⋅-1
Multiply 0 by -1.
4×2-8x-1=0
4×2-8x-1=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=-8, and c=-1 into the quadratic formula and solve for x.
8±(-8)2-4⋅(4⋅-1)2⋅4
Simplify.
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Simplify the numerator.
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Raise -8 to the power of 2.
x=8±64-4⋅(4⋅-1)2⋅4
Multiply 4 by -1.
x=8±64-4⋅-42⋅4
Multiply -4 by -4.
x=8±64+162⋅4
Add 64 and 16.
x=8±802⋅4
Rewrite 80 as 42⋅5.
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Factor 16 out of 80.
x=8±16(5)2⋅4
Rewrite 16 as 42.
x=8±42⋅52⋅4
x=8±42⋅52⋅4
Pull terms out from under the radical.
x=8±452⋅4
x=8±452⋅4
Multiply 2 by 4.
x=8±458
Simplify 8±458.
x=2±52
x=2±52
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -8 to the power of 2.
x=8±64-4⋅(4⋅-1)2⋅4
Multiply 4 by -1.
x=8±64-4⋅-42⋅4
Multiply -4 by -4.
x=8±64+162⋅4
Add 64 and 16.
x=8±802⋅4
Rewrite 80 as 42⋅5.
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Factor 16 out of 80.
x=8±16(5)2⋅4
Rewrite 16 as 42.
x=8±42⋅52⋅4
x=8±42⋅52⋅4
Pull terms out from under the radical.
x=8±452⋅4
x=8±452⋅4
Multiply 2 by 4.
x=8±458
Simplify 8±458.
x=2±52
Change the ± to +.
x=2+52
x=2+52
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -8 to the power of 2.
x=8±64-4⋅(4⋅-1)2⋅4
Multiply 4 by -1.
x=8±64-4⋅-42⋅4
Multiply -4 by -4.
x=8±64+162⋅4
Add 64 and 16.
x=8±802⋅4
Rewrite 80 as 42⋅5.
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Factor 16 out of 80.
x=8±16(5)2⋅4
Rewrite 16 as 42.
x=8±42⋅52⋅4
x=8±42⋅52⋅4
Pull terms out from under the radical.
x=8±452⋅4
x=8±452⋅4
Multiply 2 by 4.
x=8±458
Simplify 8±458.
x=2±52
Change the ± to -.
x=2-52
x=2-52
The final answer is the combination of both solutions.
x=2+52,2-52
The result can be shown in multiple forms.
Exact Form:
x=2+52,2-52
Decimal Form:
x=2.11803398…,-0.11803398…
Solve Using the Square Root Property 8x=4x^2-1

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