Question

solve the following quadratic equation for all values of x in simplest form. 5(x + 10)^2 - 24 = 26

Explanation:

Step1: Isolate the squared term

Add 24 to both sides of the equation:
$5(x + 10)^2 - 24 + 24 = 26 + 24$
Simplify: $5(x + 10)^2 = 50$

Step2: Divide by the coefficient of the squared term

Divide both sides by 5:
$\frac{5(x + 10)^2}{5} = \frac{50}{5}$
Simplify: $(x + 10)^2 = 10$

Step3: Take square roots

Take the square root of both sides:
$x + 10 = \pm\sqrt{10}$

Step4: Solve for x

Subtract 10 from both sides:
$x = -10 \pm\sqrt{10}$

Answer:

$x = -10 + \sqrt{10}$ or $x = -10 - \sqrt{10}$