use the quadratic formula to solve the equation. (enter your answers as a comma-separated list.)

\5x^2 + x = -5\

$x =$

Question

use the quadratic formula to solve the equation. (enter your answers as a comma-separated list.)

\5x^2 + x = -5\

$x =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [ "Quadratic Formula with Complex Solutions" ], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Formula with Complex Solutions", "Imaginary Numbers" ] } ## Write the equation in standard form $$ 5x^2 + x + 5 = 0 $$ ## Identify coefficients and apply the quadratic formula $$ \begin{aligned} a &= 5,\quad b = 1,\quad c = 5 \ x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-1 \pm \sqrt{1^2 - 4(5)(5)}}{2(5)} \end{aligned} $$ ## Simplify the expression $$ \begin{aligned} x &= \frac{-1 \pm \sqrt{1 - 100}}{10} \ x &= \frac{-1 \pm \sqrt{-99}}{10} \ x &= \frac{-1 \pm 3i\sqrt{11}}{10} \ x &= -\frac{1}{10} + \frac{3\sqrt{11}}{10}i, -\frac{1}{10} - \frac{3\sqrt{11}}{10}i \end{aligned} $$ Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.) $5x^2 + x = -5$ $x =$ $-\frac{1}{10} + \frac{3\sqrt{11}}{10}i, -\frac{1}{10} - \frac{3\sqrt{11}}{10}i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Formula with Complex Solutions" ] }

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QUESTION IMAGE

Question

Explanation:

Write the equation in standard form

Identify coefficients and apply the quadratic formula

Simplify the expression

Answer: