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Solve the equation
x^(2)-6x-37=0 to the nearest tenth.
Answer:
x=

Solve the equation $x^{2}-6 x-37=0$ to the nearest tenth. $\newline$ Answer: $x=$

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Solve exponential equations using logarithms

Full solution

Q. Solve the equation

x^{2}-6 x-37=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 of $ax^2 + bx + c = 0$ , where $a = 1$ , $b = -6$ , and $c = -37$ .
Use Quadratic Formula: Use the quadratic formula to solve for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Here, $a = 1$ , $b = -6$ , and $c = -37$ .
Calculate Discriminant: Calculate the discriminant $b^2 - 4ac$ . $\newline$ Discriminant = $(-6)^2 - 4(1)(-37) = 36 + 148 = 184$ .
Calculate Solutions: Calculate the two solutions using the quadratic formula. $\newline$ $x = \frac{-(-6) \pm \sqrt{184}}{2 \cdot 1}$ $\newline$ $x = \frac{6 \pm \sqrt{184}}{2}$
Calculate First Solution: Calculate the first solution (using the + sign). $\newline$ $x = \frac{6 + \sqrt{184}}{2}$ $\newline$ $x \approx \frac{6 + 13.5647}{2}$ $\newline$ $x \approx \frac{19.5647}{2}$ $\newline$ $x \approx 9.78235$ $\newline$ Round to the nearest tenth: $x \approx 9.8$
Calculate Second Solution: Calculate the second solution (using the - sign). $\newline$ $x = \frac{6 - \sqrt{184}}{2}$ $\newline$ $x \approx \frac{6 - 13.5647}{2}$ $\newline$ $x \approx \frac{-7.5647}{2}$ $\newline$ $x \approx -3.78235$ $\newline$ Round to the nearest tenth: $x \approx -3.8$

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