use completing the square to solve for $x$ in the equation $(x+7)(x-9)=25$

$x = -4$ or $6$
$x = -2$ or $14$
$x = 1 \pm \sqrt{89}$
$x = 1 \pm \sqrt{87}$

Question

use completing the square to solve for $x$ in the equation $(x+7)(x-9)=25$

$x = -4$ or $6$
$x = -2$ or $14$
$x = 1 \pm \sqrt{89}$
$x = 1 \pm \sqrt{87}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Completing the Square", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Completing the Square", "Solving Quadratic Equations" ] } ## Expand and rewrite the equation in standard form $$ \begin{aligned} (x+7)(x-9) &= 25 \ x^2 - 2x - 63 &= 25 \ x^2 - 2x - 88 &= 0 \end{aligned} $$ ## Complete the square $$ \begin{aligned} x^2 - 2x &= 88 \ x^2 - 2x + 1 &= 88 + 1 \ (x-1)^2 &= 89 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x - 1 &= \pm\sqrt{89} \ x &= 1 \pm \sqrt{89} \end{aligned} $$

$x = -4 \text{ or } 6$

$x = -2 \text{ or } 14$

$x = 1 \pm \sqrt{89}$

$x = 1 \pm \sqrt{87}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Completing the Square" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Expand and rewrite the equation in standard form

Complete the square

Solve for x

Answer: