one number is 40 more than another. their product is -400.
step 2 of 2: find the numbers by solving the equation.

Question

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", "Quadratic Word Problems" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Word Problems" ] } ## Set up the system of equations Using the **Quadratic Word Problems** knowledge point Let the two numbers be $x$ and $y$. $$ \begin{aligned} y &= x + 40 \ x \cdot y &= -400 \end{aligned} $$ ## Substitute and form a quadratic equation Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} x(x + 40) &= -400 \ x^2 + 40x + 400 &= 0 \end{aligned} $$ ## Solve the quadratic equation by factoring Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} (x + 20)^2 &= 0 \ x + 20 &= 0 \ x &= -20 \end{aligned} $$ ## Find the second number Using the **Quadratic Word Problems** knowledge point $$ \begin{aligned} y &= x + 40 \ y &= -20 + 40 \ y &= 20 \end{aligned} $$ One number is 40 more than another. Their product is $-400$. Find the numbers by solving the equation. -20 and 20 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Word Problems" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the system of equations

Substitute and form a quadratic equation

Solve the quadratic equation by factoring

Find the second number

Answer: