Solve the equation 5x^(2)+15 x-2=0 to the nearest tenth. Answer: x=

Identify Equation Type: Identify the type of equation. We have a quadratic equation in the form ax^2 + bx + c = 0, where a = 5, b = 15, and c = -2.Apply Quadratic Formula: Apply the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). We will use this to find the values of x.Substitute Values: Substitute the values of a, b, and c into the quadratic formula. x = (-(15) ± √((15)^2 - 4(5)(-2))) / (2(5))Simplify Under Square Root: Simplify under the square root. x = (-15 ± √(225 + 40)) / 10 x = (-15 ± √265) / 10Calculate Discriminant: Calculate the discriminant (√265) and simplify the equation further. x = (-15 ± √265) / 10Find Possible Values: Find the two possible values for x. x1 = (-15 + √265) / 10 x2 = (-15 - √265) / 10Calculate Numerical Values: Calculate the numerical values for x1 and x2. x1 ≈ (-15 + 16.279) / 10 x1 ≈ 1.279 / 10 x1 ≈ 0.128 x2 ≈ (-15 - 16.279) / 10 x2 ≈ -31.279 / 10 x2 ≈ -3.128Round Solutions: Round the solutions to the nearest tenth. x1 ≈ 0.1 x2 ≈ -3.1

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Solve the equation
5x^(2)+15 x-2=0 to the nearest tenth.
Answer:
x=

Solve the equation $5 x^{2}+15 x-2=0$ to the nearest tenth. $\newline$ Answer: $x=$

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Algebra 2

Solve exponential equations using common logarithms

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Q. Solve the equation

5 x^{2}+15 x-2=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 $a = 5$ , $b = 15$ , and $c = -2$ .
Apply Quadratic Formula: Apply the quadratic formula. $\newline$ The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . We will use this to find the values of $x$ .
Substitute Values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $x = \frac{{-(15) \pm \sqrt{{(15)^2 - 4(5)(-2)}}}}{{2(5)}}$
Simplify Under Square Root: Simplify under the square root. $\newline$ $x = \frac{{-15 \pm \sqrt{{225 + 40}}}}{10}$ $\newline$ $x = \frac{{-15 \pm \sqrt{265}}}{10}$
Calculate Discriminant: Calculate the discriminant ( $\sqrt{265}$ ) and simplify the equation further. $\newline$ $x = \frac{-15 \pm \sqrt{265}}{10}$
Find Possible Values: Find the two possible values for $x$ . $x_1 = \frac{{-15 + \sqrt{265}}}{{10}}$ $x_2 = \frac{{-15 - \sqrt{265}}}{{10}}$
Calculate Numerical Values: Calculate the numerical values for $x_1$ and $x_2$ .
$x_1 \approx (-15 + 16.279) / 10$
$x_1 \approx 1.279 / 10$
$x_1 \approx 0.128$

$x_2 \approx (-15 - 16.279) / 10$
$x_2 \approx -31.279 / 10$
$x_2 \approx -3.128$
Round Solutions: Round the solutions to the nearest tenth. $\newline$ $x_1 \approx 0.1$ $\newline$ $x_2 \approx -3.1$