solve for $y$.

\2y^2 - 13y + 22 = (y - 2)^2\

if there is more than one solution, separate them with commas.

Question

solve for $y$.

\2y^2 - 13y + 22 = (y - 2)^2\

if there is more than one solution, separate them with commas.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Zero Product Property", "Factoring Trinomials" ] } ## Expand the right side of the equation $$ (y - 2)^2 = y^2 - 4y + 4 $$ ## Rearrange into standard quadratic form $$ \begin{aligned} 2y^2 - 13y + 22 &= y^2 - 4y + 4 \ y^2 - 9y + 18 &= 0 \end{aligned} $$ ## Factor and solve for y $$ \begin{aligned} (y - 3)(y - 6) &= 0 \ y = 3, \quad y &= 6 \end{aligned} $$ Solve for $y$. $2y^2 - 13y + 22 = (y - 2)^2$ If there is more than one solution, separate them with commas. $y =$ 3, 6 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the right side of the equation

Rearrange into standard quadratic form

Factor and solve for y

Answer: