simplify the expression \frac{-b + \sqrt{b^2 - 4ac}}{2a} given that a = 1, b = -14, and c = -1

\frac{-b + \sqrt{b^2 - 4ac}}{2a} =
(simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using radicals and i as needed.)

Question

simplify the expression \frac{-b + \sqrt{b^2 - 4ac}}{2a} given that a = 1, b = -14, and c = -1

\frac{-b + \sqrt{b^2 - 4ac}}{2a} =
(simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using radicals and i as needed.)

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", "Simplifying Radicals" ], "new_concepts": [], "current_concepts": [ "Quadratic Formula Application", "Simplifying Radicals" ] } ## Substitute the given values into the expression $$ \begin{aligned} a &= 1,\quad b = -14,\quad c = -1 \ \frac{-b + \sqrt{b^2 - 4ac}}{2a} &= \frac{-(-14) + \sqrt{(-14)^2 - 4(1)(-1)}}{2(1)} \end{aligned} $$ ## Simplify the radicand and the fraction $$ \begin{aligned} \frac{14 + \sqrt{196 + 4}}{2} &= \frac{14 + \sqrt{200}}{2} \end{aligned} $$ ## Simplify the radical and divide $$ \begin{aligned} \sqrt{200} &= \sqrt{100 \times 2} = 10\sqrt{2} \ \frac{14 + 10\sqrt{2}}{2} &= 7 + 5\sqrt{2} \end{aligned} $$ Simplify the expression $\frac{-b + \sqrt{b^2 - 4ac}}{2a}$ given that $a = 1$, $b = -14$, and $c = -1$. $\frac{-b + \sqrt{b^2 - 4ac}}{2a} =$ $7 + 5\sqrt{2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula Application" ] }

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QUESTION IMAGE

Question

Explanation:

Substitute the given values into the expression

Simplify the radicand and the fraction

Simplify the radical and divide

Answer: