Question

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$6 x^{2}-54=0$$

Short answer

The solution is \(x = 3\) and \(x = -3\).

Step-by-step solution

Rewrite the Equation

First, rewrite the equation \(6x^{2}-54=0\) in a form where the relations between the terms are more evident, i.e. \(6x^{2}=54\).

Isolate the Term with the Variable

We try to isolate \(x^{2}\) by dividing both sides of equation by 6 to give us \(x^{2} = 9\).

Extract Square Roots

Finally, we can find the roots of the equation by taking the square root of each side. Don't forget that the square root of a number can be either positive or negative. So \(x = \pm 3\).