Question

solve $x^2 + 5 = 17$ using square roots. round your solutions to the nearest hundredth.

$\square\\ x \approx -6.12$ $\square\\ x \approx -2.12$ $\square\\ x \approx 0.24$
$\square\\ x \approx -5.48$ $\square\\ x \approx -1.48$ $\square\\ x \approx 1.48$
$\square\\ x \approx -4.78$ $\square\\ x \approx -0.24$ $\square\\ x \approx 2.12$
$\square\\ x \approx -3.46$ $\square\\ x \approx 0$ $\square\\ x \approx 3.46$

Explanation:

Step1: Isolate \(x^2\)

Subtract 5 from both sides: \(x^2 + 5 - 5 = 17 - 5\), so \(x^2 = 12\).

Step2: Take square roots

\(x = \pm\sqrt{12}\). Simplify \(\sqrt{12} \approx 3.46\) (rounded to nearest hundredth). Thus, \(x \approx 3.46\) or \(x \approx -3.46\).

Answer:

\(x \approx -3.46\), \(x \approx 3.46\)