Question

Solve the equation or write no solution. Write the solutions as integers if possible. Otherwise write them as radical expressions. $$2 s^{2}-5=27$$

Short answer

The solutions to the equation are \(s = 4\) and \(s = -4\)

Step-by-step solution

Rearrangement

First, rearrange the equation to have it equal to zero: \(2 s^{2}-5-27=0\).

Simplification

Simplify the equation by combining like terms: \(2 s^{2}-32=0\).

Isolate \(s^{2}\)

To isolate \(s^2\), we divide both sides of the equation by 2: \(s^{2}-16=0\).

Use the difference of squares

The equation now is a difference of squares, which can be factored into \((s-4)(s+4)=0\).

Solve for s

Finally, we set each factor to zero and solve for \textit{s}, giving \textit{s} = 4 and \textit{s} = -4.