Solve the equation 2x^(2)-7x-36=-2x^(2)-26 to the nearest tenth. Answer: x=

Combine Terms: Combine like terms and move all terms to one side of the equation to set it equal to zero. 2x^(2) - 7x - 36 = -2x^(2) - 26 2x^(2) + 2x^(2) - 7x - 36 + 26 = 0 4x^(2) - 7x - 10 = 0Quadratic Equation: Now, we need to solve the quadratic equation 4x^(2) - 7x - 10 = 0. We can use the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a = 4, b = -7, and c = -10.Calculate Discriminant: First, calculate the discriminant, which is b^2 - 4ac. Discriminant = (-7)^2 - 4(4)(-10) Discriminant = 49 + 160 Discriminant = 209Apply Quadratic Formula: Since the discriminant is positive, there are two real solutions. Now, apply the quadratic formula. x = [-(-7) ± sqrt(209)] / (2 * 4) x = [7 ± sqrt(209)] / 8Calculate Values: Calculate the two possible values for x. x1 = (7 + sqrt(209)) / 8 x2 = (7 - sqrt(209)) / 8Final Solutions: Use a calculator to find the numerical values to the nearest tenth. x1 ≈ (7 + 14.5) / 8 x1 ≈ 21.5 / 8 x1 ≈ 2.7 x2 ≈ (7 - 14.5) / 8 x2 ≈ -7.5 / 8 x2 ≈ -0.9

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Solve the equation
2x^(2)-7x-36=-2x^(2)-26 to the nearest tenth.
Answer:
x=

Solve the equation $2 x^{2}-7 x-36=-2 x^{2}-26$ 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}-7 x-36=-2 x^{2}-26

to the nearest tenth.

\newline

Answer:

x=

Combine Terms: Combine like terms and move all terms to one side of the equation to set it equal to zero. $\newline$ $2x^{2} - 7x - 36 = -2x^{2} - 26$ $\newline$ $2x^{2} + 2x^{2} - 7x - 36 + 26 = 0$ $\newline$ $4x^{2} - 7x - 10 = 0$
Quadratic Equation: Now, we need to solve the quadratic equation $4x^{2} - 7x - 10 = 0$ . We can use the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 4$ , $b = -7$ , and $c = -10$ .
Calculate Discriminant: First, calculate the discriminant, which is $b^2 - 4ac$ . $\newline$ Discriminant = $(-7)^2 - 4(4)(-10)$ $\newline$ Discriminant = $49 + 160$ $\newline$ Discriminant = $209$
Apply Quadratic Formula: Since the discriminant is positive, there are two real solutions. Now, apply the quadratic formula. $\newline$ $x = \frac{-(-7) \pm \sqrt{209}}{2 \cdot 4}$ $\newline$ $x = \frac{7 \pm \sqrt{209}}{8}$
Calculate Values: Calculate the two possible values for $x$ . $x_1 = \frac{7 + \sqrt{209}}{8}$ $x_2 = \frac{7 - \sqrt{209}}{8}$
Final Solutions: Use a calculator to find the numerical values to the nearest tenth. $\newline$ $x_1 \approx (7 + 14.5) / 8$ $\newline$ $x_1 \approx 21.5 / 8$ $\newline$ $x_1 \approx 2.7$ $\newline$ $x_2 \approx (7 - 14.5) / 8$ $\newline$ $x_2 \approx -7.5 / 8$ $\newline$ $x_2 \approx -0.9$