given $(x - 1)^2 = 50$, select the values of $x$.

$x = -49$
$x = 51$
$x = 1 + 5\sqrt{2}$
$x = 1 - 5\sqrt{2}$

Question

given $(x - 1)^2 = 50$, select the values of $x$.

$x = -49$
  $x = 51$
  $x = 1 + 5\sqrt{2}$
  $x = 1 - 5\sqrt{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations" ] } ## Apply the square root property $$ \begin{aligned} (x - 1)^2 &= 50 \ x - 1 &= \pm\sqrt{50} \end{aligned} $$ ## Simplify the radical expression $$ \begin{aligned} \sqrt{50} &= \sqrt{25 \times 2} = 5\sqrt{2} \ x - 1 &= \pm 5\sqrt{2} \end{aligned} $$ ## Solve for x $$ \begin{aligned} x &= 1 \pm 5\sqrt{2} \ x_1 &= 1 + 5\sqrt{2} \ x_2 &= 1 - 5\sqrt{2} \end{aligned} $$

$x = -49$

$x = 51$

$x = 1 + 5\sqrt{2}$

$x = 1 - 5\sqrt{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the square root property

Simplify the radical expression

Solve for x

Answer: