Question

solving quadratics with square roots (lev\
question\
solve the following quadratic equation\
for all values of $x$ in simplest form.\
\
$5(x - 3)^2 = 45$\
\
answer\
attempt 1 out of 2\
\
$\boldsymbol{\pm}$ $\boldsymbol{\sqrt{\quad}}$\
additional solution no solution\
$x = \square$ submit answer

Explanation:

Step1: Divide both sides by 5

To isolate the squared term, we divide each side of the equation \( 5(x - 3)^2 = 45 \) by 5. This gives us \( \frac{5(x - 3)^2}{5}=\frac{45}{5} \), which simplifies to \( (x - 3)^2 = 9 \).

Step2: Take square root of both sides

Taking the square root of both sides of the equation \( (x - 3)^2 = 9 \), we get \( x - 3=\pm\sqrt{9} \). Since \( \sqrt{9} = 3 \), this becomes \( x - 3=\pm3 \).

Step3: Solve for x (two cases)

Case 1: \( x - 3 = 3 \)

Adding 3 to both sides, we have \( x=3 + 3=6 \).

Case 2: \( x - 3=- 3 \)

Adding 3 to both sides, we get \( x=-3 + 3 = 0 \).

Answer:

\( x = 0 \) or \( x = 6 \) (or in boxed form as \( \boldsymbol{x = 0, 6} \))