solve the following quadratic function by completing the square.

\y = x^2 - 4x - 7\

\x = ? \pm \sqrt{\quad}\

Question

solve the following quadratic function by completing the square.

\y = x^2 - 4x - 7\

\x = ? \pm \sqrt{\quad}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Completing the Square", "Square Root Method" ], "new_concepts": [], "current_concepts": [ "Completing the Square", "Square Root Method", "Solving Quadratic Functions" ] } ## Set the quadratic function to zero $$ x^2 - 4x - 7 = 0 $$ ## Complete the square $$ \begin{aligned} x^2 - 4x &= 7 \ x^2 - 4x + 4 &= 7 + 4 \ (x - 2)^2 &= 11 \end{aligned} $$ ## Solve for x using square roots $$ \begin{aligned} x - 2 &= \pm\sqrt{11} \ x &= 2 \pm\sqrt{11} \end{aligned} $$ Solve the following quadratic function by completing the square. $y = x^2 - 4x - 7$ $x =$ $2$ $\pm \sqrt{\text{\quad}}$ $11$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Completing the Square" ] }

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QUESTION IMAGE

Question

Explanation:

Set the quadratic function to zero

Complete the square

Solve for x using square roots

Answer: