Solve the equation 2x^(2)+8x-17=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 = 2, b = 8, and c = -17.Use Quadratic Formula: Use the quadratic formula to solve for x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).Calculate Discriminant: Calculate the discriminant (b^2 - 4ac). Discriminant = (8)^2 - 4(2)(-17) = 64 + 136 = 200.Calculate x Values: Calculate the two possible values for x using the quadratic formula. x = (-8 ± √200) / (2 * 2) x = (-8 ± √200) / 4Simplify Square Root: Simplify the square root of the discriminant. √200 = √(100 * 2) = √100 * √2 = 10√2Substitute Simplified Root: Substitute the simplified square root back into the formula. x = (-8 ± 10√2) / 4Calculate Solutions: Calculate the two solutions for x. First solution: x = (-8 + 10√2) / 4 Second solution: x = (-8 - 10√2) / 4Simplify Solutions: Simplify both solutions. First solution: x ≈ (-8 + 14.14) / 4 ≈ 6.14 / 4 ≈ 1.5 (to the nearest tenth) Second solution: x ≈ (-8 - 14.14) / 4 ≈ -22.14 / 4 ≈ -5.5 (to the nearest tenth)

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Solve the equation
2x^(2)+8x-17=0 to the nearest tenth.
Answer:
x=

Solve the equation $2 x^{2}+8 x-17=0$ to the nearest tenth. $\newline$ Answer: $x=$

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Algebra 1

Solve linear equations: mixed review

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Q. Solve the equation

2 x^{2}+8 x-17=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 $a = 2$ , $b = 8$ , and $c = -17$ .
Use Quadratic Formula: Use the quadratic formula to solve for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Calculate Discriminant: Calculate the discriminant $(b^2 - 4ac)$ . Discriminant = $(8)^2 - 4(2)(-17) = 64 + 136 = 200$ .
Calculate x Values: Calculate the two possible values for x using the quadratic formula. $\newline$ $x = \frac{-8 \pm \sqrt{200}}{2 \times 2}$ $\newline$ $x = \frac{-8 \pm \sqrt{200}}{4}$
Simplify Square Root: Simplify the square root of the discriminant. $\newline$ $\sqrt{200} = \sqrt{(100 \cdot 2)} = \sqrt{100} \cdot \sqrt{2} = 10\sqrt{2}$
Substitute Simplified Root: Substitute the simplified square root back into the formula. $\newline$ $x = \frac{{-8 \pm 10\sqrt{2}}}{{4}}$
Calculate Solutions: Calculate the two solutions for $x$ . $\newline$ First solution: $x = \frac{{-8 + 10\sqrt{2}}}{{4}}$ $\newline$ Second solution: $x = \frac{{-8 - 10\sqrt{2}}}{{4}}$
Simplify Solutions: Simplify both solutions. $\newline$ First solution: $x \approx (-8 + 14.14) / 4 \approx 6.14 / 4 \approx 1.5$ (to the nearest tenth) $\newline$ Second solution: $x \approx (-8 - 14.14) / 4 \approx -22.14 / 4 \approx -5.5$ (to the nearest tenth)