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Solve the equation. x^2 + 4x - 9 = 0 Enter solutions like \( \frac{1+\sqrt{3}}{2} \) using (1+sqrt(3))/2...

Solve the equation.
x^2 + 4x - 9 = 0
Enter solutions like \( \frac{1+\sqrt{3}}{2} \) using (1+sqrt(3))/2 and no spaces, or enter no real solutions.

Answer

To solve the quadratic equation x2 + 4x - 9 = 0, we can use the quadratic formula:

x = \( \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

where a = 1, b = 4, and c = -9.

Calculate the discriminant:

b2 - 4ac = 42 - 4(1)(-9) = 16 + 36 = 52

Since the discriminant is positive, there are two real solutions:

  1. x = \( \frac{-4 + \sqrt{52}}{2} = \frac{-4 + 2\sqrt{13}}{2} = -2 + \sqrt{13} \)
  2. x = \( \frac{-4 - \sqrt{52}}{2} = \frac{-4 - 2\sqrt{13}}{2} = -2 - \sqrt{13} \)

Enter the solutions as -2+sqrt(13) and -2-sqrt(13).

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