Solve the equation 4x^(2)-10 x+8=-x^(2)+22 to the nearest tenth. Answer: x=

Combine like terms: Combine like terms by moving all terms to one side of the equation. We will add x^2 to both sides and subtract 22 from both sides to get all terms on the left side. 4x^2 - 10x + 8 + x^2 - 22 = 0 This simplifies to: 5x^2 - 10x - 14 = 0Solve quadratic equation: Solve the quadratic equation. We can use the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a = 5, b = -10, and c = -14. First, calculate the discriminant (b^2 - 4ac): Discriminant = (-10)^2 - 4 * 5 * (-14) Discriminant = 100 + 280 Discriminant = 380Calculate possible solutions: Calculate the two possible solutions for x using the quadratic formula. x = [-(-10) ± sqrt(380)] / (2 * 5) x = [10 ± sqrt(380)] / 10 Since we need the answer to the nearest tenth, we will calculate the square root of 380 and then divide by 10. sqrt(380) ≈ 19.5 x ≈ (10 ± 19.5) / 10Find solutions: Find the two solutions for x. First solution: x ≈ (10 + 19.5) / 10 x ≈ 29.5 / 10 x ≈ 2.95 Second solution: x ≈ (10 - 19.5) / 10 x ≈ -9.5 / 10 x ≈ -0.95

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Solve the equation
4x^(2)-10 x+8=-x^(2)+22 to the nearest tenth.
Answer:
x=

Solve the equation $4 x^{2}-10 x+8=-x^{2}+22$ to the nearest tenth. $\newline$ Answer: $x=$

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Q. Solve the equation

4 x^{2}-10 x+8=-x^{2}+22

to the nearest tenth.

\newline

Answer:

x=

Combine like terms: Combine like terms by moving all terms to one side of the equation. $\newline$ We will add $x^2$ to both sides and subtract $22$ from both sides to get all terms on the left side. $\newline$ $4x^2 - 10x + 8 + x^2 - 22 = 0$ $\newline$ This simplifies to: $\newline$ $5x^2 - 10x - 14 = 0$
Solve quadratic equation: Solve the quadratic equation. $\newline$ We can use the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 5$ , $b = -10$ , and $c = -14$ . $\newline$ First, calculate the discriminant ( $b^2 - 4ac$ ): $\newline$ Discriminant = $(-10)^2 - 4 \cdot 5 \cdot (-14)$ $\newline$ Discriminant = $100 + 280$ $\newline$ Discriminant = $380$
Calculate possible solutions: Calculate the two possible solutions for $x$ using the quadratic formula. $\newline$ $x = \frac{-(-10) \pm \sqrt{380}}{(2 \cdot 5)}$ $\newline$ $x = \frac{10 \pm \sqrt{380}}{10}$ $\newline$ Since we need the answer to the nearest tenth, we will calculate the square root of $380$ and then divide by $10$ . $\newline$ $\sqrt{380} \approx 19.5$ $\newline$ $x \approx \frac{(10 \pm 19.5)}{10}$
Find solutions: Find the two solutions for $x$ . $\newline$ First solution: $\newline$ $x \approx (10 + 19.5) / 10$ $\newline$ $x \approx 29.5 / 10$ $\newline$ $x \approx 2.95$ $\newline$ Second solution: $\newline$ $x \approx (10 - 19.5) / 10$ $\newline$ $x \approx -9.5 / 10$ $\newline$ $x \approx -0.95$