select the correct answer from each drop-down menu.

consider the following equation.
\0 = x^2 - 10x - 27\

complete each statement about the solutions to the equation.

the negative solution is between choose an answer and choose an answer.
the positive solution is between choose an answer and choose an answer.

Question

select the correct answer from each drop-down menu.

consider the following equation.
\0 = x^2 - 10x - 27\

complete each statement about the solutions to the equation.

the negative solution is between choose an answer and choose an answer.
the positive solution is between choose an answer and choose an answer.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Completing the Square" ] } ## Solve the quadratic equation using the quadratic formula $$ \begin{aligned} &x^2 - 10x - 27 = 0 \ &x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(1)(-27)}}{2(1)} \ &x = \frac{10 \pm \sqrt{100 + 108}}{2} \ &x = \frac{10 \pm \sqrt{208}}{2} \end{aligned} $$ ## Approximate the square root and find the solutions $$ \begin{aligned} &14^2 = 196,\quad 15^2 = 225 \implies 14 < \sqrt{208} < 15 \ &x_1 = \frac{10 - \sqrt{208}}{2} \implies \frac{10 - 15}{2} < x_1 < \frac{10 - 14}{2} \implies -2.5 < x_1 < -2 \ &x_2 = \frac{10 + \sqrt{208}}{2} \implies \frac{10 + 14}{2} < x_2 < \frac{10 + 15}{2} \implies 12 < x_2 < 12.5 \end{aligned} $$ ## Determine the consecutive integer bounds $$ \begin{aligned} &-3 < x_1 < -2 \ &12 < x_2 < 13 \end{aligned} $$ Consider the following equation. $$0 = x^2 - 10x - 27$$ Complete each statement about the solutions to the equation. The negative solution is between -3 and -2. The positive solution is between 12 and 13. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Solve the quadratic equation using the quadratic formula

Approximate the square root and find the solutions

Determine the consecutive integer bounds

Answer: