Question

Solve the equation. $$25 x^{2}-9=-5$$

Short answer

The solutions of the equation are \(x = 2/5\) and \(x = -2/5\).

Step-by-step solution

Write in standard form

Firstly, \( 25x^2 - 9 = -5 \) must be written in a standard form. We transpose \(-5\) to the left side of the equation to make the right hand side zero. This gives us \(25x^2 - 9 + 5 = 0 \) which simplifies further to \(25x^2 - 4 = 0 \).

Apply Square Root method

Next step is to isolate \(x^2\) by transposing \(-4\) to the right side of the equation. This gives \(25x^2 = 4 \).\n Then, divide both sides by \(25\) to completely isolate \(x^2\). So, \(x^2 = 4/25\). \n Now, take square root on both sides. In this process, remember to include both the positive and negative roots. It gives \(x = ± \sqrt{4/25}\).

Simplify the answer

After square rooting, \(x = ± \sqrt{4}/\sqrt{25} \implies x = ± 2/5 \). So, the roots of the equation are \(2/5\) and \(-2/5 \).