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Solve the equation
2x^(2)+5x+3=-7x to the nearest tenth.
Answer:
x=

Solve the equation $2 x^{2}+5 x+3=-7 x$ to the nearest tenth. $\newline$ Answer: $x=$

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Solve exponential equations using logarithms

Full solution

Q. Solve the equation

2 x^{2}+5 x+3=-7 x

to the nearest tenth.

\newline

Answer:

x=

Move Terms to One Side: First, we need to move all terms to one side of the equation to set it equal to zero. $\newline$ $2x^2 + 5x + 3 = -7x$ $\newline$ Add $7x$ to both sides to get: $\newline$ $2x^2 + 5x + 7x + 3 = 0$ $\newline$ $2x^2 + 12x + 3 = 0$
Quadratic Equation Standard Form: Now we have a quadratic equation in the standard form $ax^2 + bx + c = 0$ , where $a = 2$ , $b = 12$ , and $c = 3$ . We can solve this equation using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ First, calculate the discriminant ( $b^2 - 4ac$ ): $\newline$ Discriminant = $(12)^2 - 4(2)(3)$ $\newline$ Discriminant = $144 - 24$ $\newline$ Discriminant = $120$
Calculate Discriminant: Since the discriminant is positive, we will have two real solutions. Now we can apply the quadratic formula: $\newline$ $x = \frac{-12 \pm \sqrt{120}}{2 \times 2}$ $\newline$ $x = \frac{-12 \pm \sqrt{120}}{4}$
Apply Quadratic Formula: Next, we simplify the square root of $120$ . We can simplify $\sqrt{120}$ to $2\sqrt{30}$ to make calculations easier. $\newline$ $x = \frac{-12 \pm 2\sqrt{30}}{4}$
Simplify Square Root: Now we can simplify the equation by dividing both terms in the numerator by $4$ : $x = \frac{-3 \pm \sqrt{30}}{2}$
Divide by $4$ : Finally, we calculate the two solutions and round them to the nearest tenth: $\newline$ $x_1 = \frac{-3 + \sqrt{30}}{2}$ $\newline$ $x_1 \approx \frac{-3 + 5.477}{2}$ $\newline$ $x_1 \approx \frac{2.477}{2}$ $\newline$ $x_1 \approx 1.2$ $\newline$ $x_2 = \frac{-3 - \sqrt{30}}{2}$ $\newline$ $x_2 \approx \frac{-3 - 5.477}{2}$ $\newline$ $x_2 \approx \frac{-8.477}{2}$ $\newline$ $x_2 \approx -4.2$

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