How do you solve $- \sqrt{x} = - 25 x$ $-sqrtx = -25x$ ?

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How do you solve $- \sqrt{x} = - 25 x$ $-sqrtx = -25x$ ?

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Answer 1 · 2015-08-05T18:52:05

$x = 0$ $x = 0$ and $x = \frac{1}{625}$ $x= 1/625$

Explanation:

First, rewrite your equation by cancelling the minus sign

$\sqrt{x} = 25 x$ $sqrt(x) = 25x$

Right from the start, it's obvious that any solution you find must be positive, $x \geq 0$ $x>=0$ , since the square root of a negative number does not have a real number as a solution.

So, square both sides of the equation to get

${(\sqrt{x})}^{2} = {(25 x)}^{2}$ $(sqrt(x))^2 = (25x)^2$

$x = 625 x^{2}$ $x = 625x^2$

Move everything to one side of the equation and factor the resulting expression

$625 x^{2} - x = 0$ $625x^2 - x = 0$

$x (625 x - 1) = 0$ $x(625x - 1) = 0$

This equation is equal to zero when wither $x = 0$ $x=0$ or when $(625 x - 1) = 0$ $(625x-1)=0$ , which is equivalent to having

$625 x - 1 = 0 \Rightarrow x = \frac{1}{625}$ $625x-1 = 0 => x= 1/625$

Both solutions are valid because they satisfy the condition $x \geq 0$ $x>=0$ .

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How do you solve $- \sqrt{x} = - 25 x$ $-sqrtx = -25x$ ?

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Explanation:

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