Solve the equation 5x^(2)+14 x-4=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 = 14, and c = -4.Use Quadratic Formula: Use the quadratic formula to solve for x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).Substitute Values: Substitute the values of a, b, and c into the quadratic formula. x = (-(14) ± √((14)^2 - 4(5)(-4))) / (2(5))Simplify Square Root: Simplify under the square root. x = (-14 ± √(196 + 80)) / 10 x = (-14 ± √(276)) / 10Calculate Discriminant: Calculate the discriminant (√(276)). √(276) ≈ 16.613Solve for Positive x: Solve for x using the positive part of the ± symbol. x = (-14 + 16.613) / 10 x = 2.613 / 10 x = 0.2613Solve for Negative x: Solve for x using the negative part of the ± symbol. x = (-14 - 16.613) / 10 x = -30.613 / 10 x = -3.0613Round Solutions: Round both solutions to the nearest tenth. x ≈ 0.3 and x ≈ -3.1

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Solve the equation
5x^(2)+14 x-4=0 to the nearest tenth.
Answer:
x=

Solve the equation $5 x^{2}+14 x-4=0$ 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}+14 x-4=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 $a = 5$ , $b = 14$ , and $c = -4$ .
Use Quadratic Formula: Use the quadratic formula to solve for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute Values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $x = \frac{{-(14) \pm \sqrt{{(14)^2 - 4(5)(-4)}}}}{{2(5)}}$
Simplify Square Root: Simplify under the square root. $\newline$ $x = \frac{{-14 \pm \sqrt{{196 + 80}}}}{10}$ $\newline$ $x = \frac{{-14 \pm \sqrt{{276}}}}{10}$
Calculate Discriminant: Calculate the discriminant ( $\sqrt{276}$ ). $\newline$ $\sqrt{276} \approx 16.613$
Solve for Positive $x$ : Solve for $x$ using the positive part of the $\pm$ symbol. $\newline$ $x = \frac{{-14 + 16.613}}{{10}}$ $\newline$ $x = \frac{{2.613}}{{10}}$ $\newline$ $x = 0.2613$
Solve for Negative x: Solve for x using the negative part of the $\pm$ symbol. $\newline$ $x = (-14 - 16.613) / 10$ $\newline$ $x = -30.613 / 10$ $\newline$ $x = $-3$.$0613$
Round Solutions: Round both solutions to the nearest tenth. $\newline$$x \approx 0.3$ and $x \approx -3.1$