Question

solving quadratics with square roots (lev\
question\
solve the following quadratic equation\
for all values of $x$ in simplest form.\
\\5(x^2 - 7) - 1 = 9\\\
answer\
attempt 1 out of 2\
\\(\boldsymbol{\oplus}\\) additional solution \\(\boldsymbol{\ominus}\\) no solution\
\\(x = \\)\
submit answer

Explanation:

Step1: Simplify the equation

First, we simplify the left - hand side of the equation \(5(x^{2}-7)-1 = 9\).
First, distribute the 5: \(5x^{2}-35 - 1=9\).
Then, combine like terms: \(5x^{2}-36 = 9\).

Step2: Isolate the \(x^{2}\) term

Add 36 to both sides of the equation: \(5x^{2}=9 + 36\).
\(5x^{2}=45\).
Then, divide both sides by 5: \(x^{2}=\frac{45}{5}=9\).

Step3: Solve for \(x\)

Take the square root of both sides. Remember that when we take the square root of a number, we have two solutions (positive and negative).
\(x=\pm\sqrt{9}=\pm3\).

Answer:

\(x = \pm3\)