QuestionJuly 14, 2025

Check for Understanding Instructions: Solve -5x^2-3x-1=0 using the quadratic formula. a=-5 b=-3 c=-1 x=(square +square sqrt (11))/(square ) x=(square -square sqrt (11))/(square )

Check for Understanding Instructions: Solve -5x^2-3x-1=0 using the quadratic formula. a=-5 b=-3 c=-1 x=(square +square sqrt (11))/(square ) x=(square -square sqrt (11))/(square )
Check for Understanding Instructions: Solve -5x^2-3x-1=0 using the quadratic formula. a=-5 b=-3 c=-1 x=(square +square sqrt (11))/(square ) x=(square -square sqrt (11))/(square )

Solution
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Answer

x = \frac{3 + i\sqrt{11}}{-10}, x = \frac{3 - i\sqrt{11}}{-10} Explanation 1. Identify coefficients Given a = -5, b = -3, c = -1. 2. Apply the quadratic formula The quadratic formula is **x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}**. 3. Calculate discriminant b^2 - 4ac = (-3)^2 - 4(-5)(-1) = 9 - 20 = -11. 4. Substitute into the quadratic formula x = \frac{-(-3) \pm \sqrt{-11}}{2(-5)} = \frac{3 \pm i\sqrt{11}}{-10}.

Explanation

1. Identify coefficients<br /> Given $a = -5$, $b = -3$, $c = -1$.<br /><br />2. Apply the quadratic formula<br /> The quadratic formula is **$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**.<br /><br />3. Calculate discriminant<br /> $b^2 - 4ac = (-3)^2 - 4(-5)(-1) = 9 - 20 = -11$.<br /><br />4. Substitute into the quadratic formula<br /> $x = \frac{-(-3) \pm \sqrt{-11}}{2(-5)} = \frac{3 \pm i\sqrt{11}}{-10}$.
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