Solve using the quadratic formula. $\newline$ $m^{2}+8m+9=0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $m=\square \text{ or } m=$

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Solve a quadratic equation using the quadratic formula

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Q. Solve using the quadratic formula.

\newline

m^{2}+8m+9=0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

m=\square \text{ or } m=

Identify coefficients: Identify the coefficients of the quadratic equation. $\newline$ The quadratic equation is in the form of $ax^2 + bx + c = 0$ . For the equation $m^2 + 8m + 9 = 0$ , the coefficients are: $\newline$ a = $1$ (coefficient of $m^2$ ) $\newline$ b = $8$ (coefficient of $m$ ) $\newline$ c = $9$ (constant term)
Write formula: Write down the quadratic formula. $\newline$ The quadratic formula is $m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute coefficients: Substitute the coefficients into the quadratic formula. $\newline$ Using the values of $a$ , $b$ , and $c$ from Step $1$ , we get: $\newline$ $m = (-(8) \pm \sqrt{(8)^2 - 4(1)(9)}) / (2(1))$
Simplify square root: Simplify under the square root. $\newline$ Calculate the discriminant (the expression under the square root): $\newline$ $(8)^2 - 4(1)(9) = 64 - 36 = 28$
Insert discriminant: Insert the discriminant into the formula. $\newline$ $m = \frac{-8 \pm \sqrt{28}}{2}$
Simplify equation: Simplify the square root. $\newline$ $\sqrt{28}$ can be simplified to $\sqrt{(4\times7)}$ which is $2\sqrt{7}$ . $\newline$ $m = \frac{-8 \pm 2\sqrt{7}}{2}$
Write solutions: Simplify the equation by dividing by $2$ . $\newline$ $m = \frac{-4 \pm \sqrt{7}}{2}$
Write solutions: Simplify the equation by dividing by $2$ . $m = (-4 \pm \sqrt{7})$ Write the final solutions. The solutions are $m = -4 + \sqrt{7}$ and $m = -4 - \sqrt{7}$ . These cannot be simplified to integers or fractions, so we will leave them in this form or convert them to decimal form if necessary.