Question

question
solve for ( a ). express your answer as an integer or integers or in simplest radical form.
( -176 = -5a^2 + 4 )

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \(a^2\), we subtract 4 from both sides of the equation \(-176 = -5a^2 + 4\).

$$ -176 - 4=-5a^2+4 - 4 $$

Simplifying both sides gives:

$$ -180=-5a^2 $$

Step2: Divide both sides by -5

To solve for \(a^2\), we divide both sides of the equation \(-180 = -5a^2\) by -5.

$$ \frac{-180}{-5}=\frac{-5a^2}{-5} $$

Simplifying both sides gives:

$$ 36 = a^2 $$

Step3: Take square root of both sides

To solve for \(a\), we take the square root of both sides of the equation \(36 = a^2\). Remember that when we take the square root of a number, we get both a positive and a negative solution.

$$ a=\pm\sqrt{36} $$

Since \(\sqrt{36} = 6\), we have:

$$ a=\pm6 $$

Answer:

\(a = 6\) or \(a = -6\)