Question

Solve the quadratic equation by finding square roots or by using the quadratic formula. Explain why you chose the method. $$5 x^{2}=25$$

Short answer

The solutions to the quadratic equation \(5x^2 = 25\) are \(x = \sqrt {5}\) or \(x = -\sqrt {5}\), which can also be represented as \(x = - 2.236067977\) and \(x = 2.236067977\).

Step-by-step solution

Understand the equation

The equation given is \(5x^2 = 25\). This is a quadratic equation because it is of the form \(ax^2 = c\), where \(a\) and \(c\) are numbers.

Isolate x^2

To isolate \(x^2\), divide both sides of the equation by 5. Then you will get \(x^2 = 5\). This isolates \(x^2\) by itself on one side of the equation.

Use the square root property

Next, you can find \(x\) by finding the square root of both sides of the equation. However, when square rooting, one must consider both the positive and negative roots. This will yield \(x = \sqrt {5}\) or \(x = -\sqrt {5}\).

Rationalize the denominator (Optional)

The solutions can be left as \(x = -\sqrt {5}\) and \(x = \sqrt {5}\). But in case if the answer needs to be provided in simplified radical form or decimal form, rationalize the denominator which gives two possible solutions for this quadratic equation: \(x = - 2.236067977\) and \(x = 2.236067977\) .