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Solve the equation
x^(2)+17 x+40=0 to the nearest tenth.
Answer:
x=

Solve the equation $x^{2}+17 x+40=0$ to the nearest tenth. $\newline$ Answer: $x=$

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Solve exponential equations using logarithms

Full solution

Q. Solve the equation

x^{2}+17 x+40=0

to the nearest tenth.

\newline

Answer:

x=

Identify Equation Type: Identify the type of equation. $\newline$ We have a quadratic equation in the form $ax^2 + bx + c = 0$ , where $a = 1$ , $b = 17$ , and $c = 40$ .
Apply Quadratic Formula: Apply the quadratic formula to find the solutions for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Here, $a = 1$ , $b = 17$ , and $c = 40$ .
Calculate Discriminant: Calculate the discriminant $b^2 - 4ac$ . $\newline$ Discriminant = $17^2 - 4(1)(40) = 289 - 160 = 129$ .
Calculate Solutions: Calculate the two solutions using the quadratic formula. $\newline$ $x = \frac{-17 \pm \sqrt{129}}{2 \times 1}$ $\newline$ $x = \frac{-17 \pm \sqrt{129}}{2}$
Calculate First Solution: Calculate the first solution (using the positive square root). $\newline$ $x = \frac{-17 + \sqrt{129}}{2}$ $\newline$ $x \approx \frac{-17 + 11.3578}{2}$ $\newline$ $x \approx \frac{-5.6422}{2}$ $\newline$ $x \approx -2.8211$ $\newline$ Round to the nearest tenth: $x \approx -2.8$
Calculate Second Solution: Calculate the second solution (using the negative square root). $\newline$ $x = \frac{{-17 - \sqrt{129}}}{{2}}$ $\newline$ $x \approx \frac{{-17 - 11.3578}}{{2}}$ $\newline$ $x \approx \frac{{-28.3578}}{{2}}$ $\newline$ $x \approx -14.1789$ $\newline$ Round to the nearest tenth: $x \approx -14.2$

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