QuestionAugust 27, 2025

Find the solutions to the quadratic equation m^2+8m+15=0 m=-3 or m=5 m=-3 or m=-5 m=3 or m=5 m=3 or m=-5

Find the solutions to the quadratic equation m^2+8m+15=0 m=-3 or m=5 m=-3 or m=-5 m=3 or m=5 m=3 or m=-5
Find the solutions to the quadratic equation m^2+8m+15=0 m=-3 or m=5 m=-3 or m=-5 m=3 or m=5 m=3 or m=-5

Solution
3.7(269 votes)

Answer

m = -3 or m = -5 Explanation 1. Identify coefficients The quadratic equation is m^2 + 8m + 15 = 0. Here, a = 1, b = 8, and c = 15. 2. Use the quadratic formula The solutions are given by **m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}**. Substitute a, b, and c into the formula. 3. Calculate the discriminant Compute b^2 - 4ac = 8^2 - 4 \cdot 1 \cdot 15 = 64 - 60 = 4. 4. Solve for m Substitute the discriminant back into the quadratic formula: m = \frac{-8 \pm \sqrt{4}}{2 \cdot 1} = \frac{-8 \pm 2}{2}. 5. Find the two solutions m_1 = \frac{-8 + 2}{2} = \frac{-6}{2} = -3. m_2 = \frac{-8 - 2}{2} = \frac{-10}{2} = -5.

Explanation

1. Identify coefficients<br /> The quadratic equation is $m^2 + 8m + 15 = 0$. Here, $a = 1$, $b = 8$, and $c = 15$.<br /><br />2. Use the quadratic formula<br /> The solutions are given by **$m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**. Substitute $a$, $b$, and $c$ into the formula.<br /><br />3. Calculate the discriminant<br /> Compute $b^2 - 4ac = 8^2 - 4 \cdot 1 \cdot 15 = 64 - 60 = 4$.<br /><br />4. Solve for $m$<br /> Substitute the discriminant back into the quadratic formula: <br /> $m = \frac{-8 \pm \sqrt{4}}{2 \cdot 1} = \frac{-8 \pm 2}{2}$.<br /><br />5. Find the two solutions<br /> $m_1 = \frac{-8 + 2}{2} = \frac{-6}{2} = -3$.<br /> $m_2 = \frac{-8 - 2}{2} = \frac{-10}{2} = -5$.
Click to rate:

Similar Questions