Question

Choose a method to solve the quadratic equation. Explain your choice. $$9 a^{2}-25=0$$

Short answer

The solutions to the quadratic equation given are \(a = -5/3\) and \(a = 5/3\).

Step-by-step solution

Simplify The Equation

The equation \(9a^{2}-25=0\) can be written in its difference of squares form, as \((3a+5)(3a-5)= 0\).

Equate Each Factor to Zero

Set each factor to equal zero, this gives two equations: \(3a+5= 0\) and \(3a -5=0\).

Solve for the Variable

Solving each equation will gives the two roots of the quadratic equation. For \(3a + 5 = 0\), isolating \(a\) gives \(a = -5/3\). Similarly, for \(3a - 5 = 0\), isolating \(a\) gives \(a = 5/3\).