Question

question
solve the following quadratic equation for all values of $x$ in simplest form.
$5(3x - 3)^2 - 44 = -29$
answer attempt 1 out of 2
○ additional solution ○ no solution
$x = $
± $\sqrt{}$

Explanation:

Step1: Isolate the squared term

Add 44 to both sides:
$5(3x-3)^2 = -29 + 44$
$5(3x-3)^2 = 15$

Step2: Simplify the equation

Divide both sides by 5:
$(3x-3)^2 = \frac{15}{5}$
$(3x-3)^2 = 3$

Step3: Take square roots

Take square root of both sides:
$3x-3 = \pm\sqrt{3}$

Step4: Isolate the variable term

Add 3 to both sides:
$3x = 3 \pm\sqrt{3}$

Step5: Solve for x

Divide both sides by 3:
$x = \frac{3 \pm\sqrt{3}}{3}$
$x = 1 \pm \frac{\sqrt{3}}{3}$
Or simplified:
$x = \frac{3+\sqrt{3}}{3}$ and $x = \frac{3-\sqrt{3}}{3}$

Answer:

$x=2$ and $x=1$