QuestionAugust 27, 2025

Solve the quadratic equation: x^2-9x-36=0 x=-3,x=12 x=-2,x=3 x=-12,x=-3 x=12,x=3

Solve the quadratic equation: x^2-9x-36=0 x=-3,x=12 x=-2,x=3 x=-12,x=-3 x=12,x=3
Solve the quadratic equation: x^2-9x-36=0 x=-3,x=12 x=-2,x=3 x=-12,x=-3 x=12,x=3

Solution
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Answer

x = 12, x = -3 Explanation 1. Identify coefficients The quadratic equation is x^2 - 9x - 36 = 0. Here, a = 1, b = -9, and c = -36. 2. Apply the quadratic formula Use **x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}**. Substitute a = 1, b = -9, c = -36. 3. Calculate discriminant b^2 - 4ac = (-9)^2 - 4(1)(-36) = 81 + 144 = 225. 4. Solve for roots x = \frac{9 \pm \sqrt{225}}{2} = \frac{9 \pm 15}{2}. 5. Find solutions x_1 = \frac{9 + 15}{2} = 12, x_2 = \frac{9 - 15}{2} = -3.

Explanation

1. Identify coefficients<br /> The quadratic equation is $x^2 - 9x - 36 = 0$. Here, $a = 1$, $b = -9$, and $c = -36$.<br />2. Apply the quadratic formula<br /> Use **$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$**. Substitute $a = 1$, $b = -9$, $c = -36$.<br />3. Calculate discriminant<br /> $b^2 - 4ac = (-9)^2 - 4(1)(-36) = 81 + 144 = 225$.<br />4. Solve for roots<br /> $x = \frac{9 \pm \sqrt{225}}{2} = \frac{9 \pm 15}{2}$.<br />5. Find solutions<br /> $x_1 = \frac{9 + 15}{2} = 12$, $x_2 = \frac{9 - 15}{2} = -3$.
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