Question

Use factoring to solve the equation. Use a graphing calculator to check your solution if you wish. $$25 x^{2}-4=0$$

Short answer

The roots of the given quadratic equation \(25x^{2}-4=0\) are \(x = 0.4\) and \(x = -0.4\).

Step-by-step solution

Identifying the Model

The equation is given as \(25x^{2}-4=0\). This fits the general common type for difference of squares \(a^{2}-b^{2}\). Therefore, it can be written in the form \((mx-n)(mx+n) = 0\).

Factoring the Equation

Calculating the square roots of \(a = 25\) and \(b = 4\), we get \(m = 5\) and \(n = 2\), respectively. Substituting these into the factorised form we get \((5x - 2)(5x + 2) = 0\).

Solving for x

To find the roots of the equation, each of the factors are equated to zero and simplified to find the value of \(x\). This gives us \(5x - 2 = 0\) and \(5x + 2 = 0\). Solving these two equations, we find \(x = 0.4\) and \(x = -0.4\), respectively.