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8x+4-\left(8x-4\right)=\left(2x-1\right)\left(2x+1\right)
Variable x cannot be equal to any of the values -\frac{1}{2},\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 4\left(2x-1\right)\left(2x+1\right), the least common multiple of 2x-1,2x+1,4.
8x+4-8x+4=\left(2x-1\right)\left(2x+1\right)
To find the opposite of 8x-4, find the opposite of each term.
4+4=\left(2x-1\right)\left(2x+1\right)
Combine 8x and -8x to get 0.
8=\left(2x-1\right)\left(2x+1\right)
Add 4 and 4 to get 8.
8=\left(2x\right)^{2}-1
Consider \left(2x-1\right)\left(2x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
8=2^{2}x^{2}-1
Expand \left(2x\right)^{2}.
8=4x^{2}-1
Calculate 2 to the power of 2 and get 4.
4x^{2}-1=8
Swap sides so that all variable terms are on the left hand side.
4x^{2}=8+1
Add 1 to both sides.
4x^{2}=9
Add 8 and 1 to get 9.
x^{2}=\frac{9}{4}
Divide both sides by 4.
x=\frac{3}{2} x=-\frac{3}{2}
Take the square root of both sides of the equation.
8x+4-\left(8x-4\right)=\left(2x-1\right)\left(2x+1\right)
Variable x cannot be equal to any of the values -\frac{1}{2},\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 4\left(2x-1\right)\left(2x+1\right), the least common multiple of 2x-1,2x+1,4.
8x+4-8x+4=\left(2x-1\right)\left(2x+1\right)
To find the opposite of 8x-4, find the opposite of each term.
4+4=\left(2x-1\right)\left(2x+1\right)
Combine 8x and -8x to get 0.
8=\left(2x-1\right)\left(2x+1\right)
Add 4 and 4 to get 8.
8=\left(2x\right)^{2}-1
Consider \left(2x-1\right)\left(2x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
8=2^{2}x^{2}-1
Expand \left(2x\right)^{2}.
8=4x^{2}-1
Calculate 2 to the power of 2 and get 4.
4x^{2}-1=8
Swap sides so that all variable terms are on the left hand side.
4x^{2}-1-8=0
Subtract 8 from both sides.
4x^{2}-9=0
Subtract 8 from -1 to get -9.
x=\frac{0±\sqrt{0^{2}-4\times 4\left(-9\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\left(-9\right)}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\left(-9\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{144}}{2\times 4}
Multiply -16 times -9.
x=\frac{0±12}{2\times 4}
Take the square root of 144.
x=\frac{0±12}{8}
Multiply 2 times 4.
x=\frac{3}{2}
Now solve the equation x=\frac{0±12}{8} when ± is plus. Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.
x=-\frac{3}{2}
Now solve the equation x=\frac{0±12}{8} when ± is minus. Reduce the fraction \frac{-12}{8} to lowest terms by extracting and canceling out 4.
x=\frac{3}{2} x=-\frac{3}{2}
The equation is now solved.