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4=2x\times 5x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x.
4=2x^{2}\times 5
Multiply x and x to get x^{2}.
4=10x^{2}
Multiply 2 and 5 to get 10.
10x^{2}=4
Swap sides so that all variable terms are on the left hand side.
x^{2}=\frac{4}{10}
Divide both sides by 10.
x^{2}=\frac{2}{5}
Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.
x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}
Take the square root of both sides of the equation.
4=2x\times 5x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x.
4=2x^{2}\times 5
Multiply x and x to get x^{2}.
4=10x^{2}
Multiply 2 and 5 to get 10.
10x^{2}=4
Swap sides so that all variable terms are on the left hand side.
10x^{2}-4=0
Subtract 4 from both sides.
x=\frac{0±\sqrt{0^{2}-4\times 10\left(-4\right)}}{2\times 10}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 10\left(-4\right)}}{2\times 10}
Square 0.
x=\frac{0±\sqrt{-40\left(-4\right)}}{2\times 10}
Multiply -4 times 10.
x=\frac{0±\sqrt{160}}{2\times 10}
Multiply -40 times -4.
x=\frac{0±4\sqrt{10}}{2\times 10}
Take the square root of 160.
x=\frac{0±4\sqrt{10}}{20}
Multiply 2 times 10.
x=\frac{\sqrt{10}}{5}
Now solve the equation x=\frac{0±4\sqrt{10}}{20} when ± is plus.
x=-\frac{\sqrt{10}}{5}
Now solve the equation x=\frac{0±4\sqrt{10}}{20} when ± is minus.
x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}
The equation is now solved.