Question

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use the quadratic formula to solve (x^2 + 8x + 9 = 0).
what are the solutions to the equation?
round irrational solutions to the nearest tenth.
(x = -6.6) and (x = -1.4)
(x = -1) and (x = -8)
(x = -1.2) and (x = -6.8)
x = 1 and (x = -9)

Explanation:

Step1: Recall quadratic formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For the equation \(x^{2}+8x + 9 = 0\), we have \(a = 1\), \(b = 8\), and \(c = 9\).

Step2: Calculate discriminant

First, calculate the discriminant \(D=b^{2}-4ac\). Substituting the values, we get \(D = 8^{2}-4\times1\times9=64 - 36=28\).

Step3: Substitute into quadratic formula

Now, substitute \(a = 1\), \(b = 8\), and \(D = 28\) into the quadratic formula: \(x=\frac{-8\pm\sqrt{28}}{2\times1}=\frac{-8\pm2\sqrt{7}}{2}=-4\pm\sqrt{7}\).

Step4: Approximate the values

We know that \(\sqrt{7}\approx2.6458\). So, \(x=-4 + 2.6458\approx - 1.4\) and \(x=-4-2.6458\approx - 6.6\).

Answer:

\(x = - 6.6\) and \(x=-1.4\) (corresponding to the first option: \(x = - 6.6\) and \(x=-1.4\))