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x\times 4x=1
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,2x.
x^{2}\times 4=1
Multiply x and x to get x^{2}.
x^{2}=\frac{1}{4}
Divide both sides by 4.
x=\frac{1}{2} x=-\frac{1}{2}
Take the square root of both sides of the equation.
x\times 4x=1
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,2x.
x^{2}\times 4=1
Multiply x and x to get x^{2}.
x^{2}\times 4-1=0
Subtract 1 from both sides.
4x^{2}-1=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
x=\frac{0±\sqrt{0^{2}-4\times 4\left(-1\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\left(-1\right)}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\left(-1\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{16}}{2\times 4}
Multiply -16 times -1.
x=\frac{0±4}{2\times 4}
Take the square root of 16.
x=\frac{0±4}{8}
Multiply 2 times 4.
x=\frac{1}{2}
Now solve the equation x=\frac{0±4}{8} when ± is plus. Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.
x=-\frac{1}{2}
Now solve the equation x=\frac{0±4}{8} when ± is minus. Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.
x=\frac{1}{2} x=-\frac{1}{2}
The equation is now solved.