one number is 18 more than another. their product is -81.
step 2 of 2: find the numbers by solving the equation.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Integer Word Problems" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Integer Word Problems", "Factoring Quadratic Equations" ] } ## Set up the system of equations Using the *Integer Word Problems* knowledge point Let the two numbers be $x$ and $y$. $$ \begin{aligned} y &= x + 18 \ x \cdot y &= -81 \end{aligned} $$ ## Substitute and form a quadratic equation Using the *Solving Quadratic Equations* knowledge point $$ \begin{aligned} x(x + 18) &= -81 \ x^2 + 18x + 81 &= 0 \end{aligned} $$ ## Solve the quadratic equation Using the *Factoring Quadratic Equations* knowledge point $$ \begin{aligned} (x + 9)^2 &= 0 \ x &= -9 \end{aligned} $$ ## Find the second number Using the *Integer Word Problems* knowledge point $$ \begin{aligned} y &= -9 + 18 \ y &= 9 \end{aligned} $$ One number is 18 more than another. Their product is $-81$. Step 2 of 2 : Find the numbers by solving the equation. -9 and 9 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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Question

Explanation:

Set up the system of equations

Substitute and form a quadratic equation

Solve the quadratic equation

Find the second number

Answer: