apply the square root principle to solve $(x - 5)^2 - 40 = 0$.

a) $x = -5 + 2\sqrt{10}$, $x = -5 - 2\sqrt{10}$

b) $x = -5 + 2i\sqrt{10}$, $x = -5 - 2i\sqrt{10}$

c) $x = 5 + 2i\sqrt{10}$, $x = 5 - 2i\sqrt{10}$

d) $x = 5 + 2\sqrt{10}$, $x = 5 - 2\sqrt{10}$

Question

apply the square root principle to solve $(x - 5)^2 - 40 = 0$.

a) $x = -5 + 2\sqrt{10}$, $x = -5 - 2\sqrt{10}$

b) $x = -5 + 2i\sqrt{10}$, $x = -5 - 2i\sqrt{10}$

c) $x = 5 + 2i\sqrt{10}$, $x = 5 - 2i\sqrt{10}$

d) $x = 5 + 2\sqrt{10}$, $x = 5 - 2\sqrt{10}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Square Root Principle" ], "new_concepts": [], "current_concepts": [ "Square Root Principle", "Simplifying Radicals" ] } ## Isolate the squared term Using the *Square Root Principle* knowledge point $$ \begin{aligned} (x - 5)^2 - 40 &= 0 \ (x - 5)^2 &= 40 \end{aligned} $$ ## Apply the square root principle Using the *Square Root Principle* knowledge point $$ \begin{aligned} x - 5 &= \pm\sqrt{40} \end{aligned} $$ ## Simplify the radical Using the *Square Root Principle* knowledge point $$ \begin{aligned} \sqrt{40} &= \sqrt{4 \times 10} = 2\sqrt{10} \ x - 5 &= \pm 2\sqrt{10} \end{aligned} $$ ## Solve for x Using the *Square Root Principle* knowledge point $$ \begin{aligned} x &= 5 \pm 2\sqrt{10} \ x = 5 + 2\sqrt{10} &,\quad x = 5 - 2\sqrt{10} \end{aligned} $$

A) $x = -5 + 2\sqrt{10}$ , $x = -5 - 2\sqrt{10}$

B) $x = -5 + 2i\sqrt{10}$ , $x = -5 - 2i\sqrt{10}$

C) $x = 5 + 2i\sqrt{10}$ , $x = 5 - 2i\sqrt{10}$

D) $x = 5 + 2\sqrt{10}$ , $x = 5 - 2\sqrt{10}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Principle" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the squared term

Apply the square root principle

Simplify the radical

Solve for x

Answer: