Question

question 9 of 10 step 1 of 1 solve the quadratic equation by the square root method and write the solutions in radical form. simplify the solutions. (4x + 11)² = 50 answer 2 points x = or keypad keyboard shortcuts

Explanation:

Step1: Take square roots of both sides

$$4x + 11 = \pm\sqrt{50}$$

Step2: Simplify the radical

$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$, so:
$$4x + 11 = \pm5\sqrt{2}$$

Step3: Isolate the term with $x$

$$4x = -11 \pm5\sqrt{2}$$

Step4: Solve for $x$

$$x = \frac{-11 \pm5\sqrt{2}}{4}$$

Answer:

$x = \frac{-11 + 5\sqrt{2}}{4}$ or $x = \frac{-11 - 5\sqrt{2}}{4}$