QuestionJuly 15, 2025

Solve by using the quadratic formula. w^2=-6w-11 Separate your answers with commas, if necessary. Express the solution set in exact simplest form. The solution set is square

Solve by using the quadratic formula. w^2=-6w-11 Separate your answers with commas, if necessary. Express the solution set in exact simplest form. The solution set is square
Solve by using the quadratic formula.
w^2=-6w-11
Separate your answers with commas, if necessary.
Express the solution set in exact simplest form.
The solution set is square

Solution
4.4(155 votes)

Answer

-3 + i\sqrt{2}, -3 - i\sqrt{2} Explanation 1. Rearrange the equation Move all terms to one side: w^2 + 6w + 11 = 0. 2. Identify coefficients a = 1, b = 6, c = 11. 3. Apply quadratic formula Use **w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}**. 4. Calculate discriminant b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot 11 = 36 - 44 = -8. 5. Compute solutions w = \frac{-6 \pm \sqrt{-8}}{2} = \frac{-6 \pm 2i\sqrt{2}}{2}. 6. Simplify solutions w = -3 \pm i\sqrt{2}.

Explanation

1. Rearrange the equation<br /> Move all terms to one side: $w^2 + 6w + 11 = 0$.<br />2. Identify coefficients<br /> $a = 1$, $b = 6$, $c = 11$.<br />3. Apply quadratic formula<br /> Use **$w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**.<br />4. Calculate discriminant<br /> $b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot 11 = 36 - 44 = -8$.<br />5. Compute solutions<br /> $w = \frac{-6 \pm \sqrt{-8}}{2} = \frac{-6 \pm 2i\sqrt{2}}{2}$.<br />6. Simplify solutions<br /> $w = -3 \pm i\sqrt{2}$.
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