Solve the equation -2x^(2)+7x-1=-3x^(2)+14 to the nearest tenth. Answer: x=

Set Equation to Zero: First, we need to set the equation to zero by moving all terms to one side of the equation. -2x^2 + 7x - 1 - (-3x^2 + 14) = 0Simplify Equation: Simplify the equation by combining like terms. -2x^2 + 7x - 1 + 3x^2 - 14 = 0Combine Terms: Combine the x^2 terms and the constant terms. (3x^2 - 2x^2) + 7x - (14 + 1) = 0 x^2 + 7x - 15 = 0Solve Quadratic Equation: Now we need to solve the quadratic equation x^2 + 7x - 15 = 0. We can use the quadratic formula, where a = 1, b = 7, and c = -15. x = [-b ± sqrt(b^2 - 4ac)] / (2a)Substitute Values: Substitute the values of a, b, and c into the quadratic formula. x = [-7 ± sqrt(7^2 - 4(1)(-15))] / (2(1))Calculate Discriminant: Calculate the discriminant (the part under the square root). Discriminant = 7^2 - 4(1)(-15) = 49 + 60 = 109Substitute Discriminant: Substitute the discriminant back into the quadratic formula. x = [-7 ± sqrt(109)] / 2Calculate Solutions: Calculate the two possible solutions for x. x = (-7 + sqrt(109)) / 2 or x = (-7 - sqrt(109)) / 2Find Numerical Values: Use a calculator to find the numerical values of x to the nearest tenth. x ≈ (-7 + 10.4) / 2 or x ≈ (-7 - 10.4) / 2 x ≈ 1.7 or x ≈ -8.7

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Solve the equation
-2x^(2)+7x-1=-3x^(2)+14 to the nearest tenth.
Answer:
x=

Solve the equation $-2 x^{2}+7 x-1=-3 x^{2}+14$ to the nearest tenth. $\newline$ Answer: $x=$

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Algebra 2

Csc, sec, and cot of special angles

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Q. Solve the equation

-2 x^{2}+7 x-1=-3 x^{2}+14

to the nearest tenth.

\newline

Answer:

x=

Set Equation to Zero: First, we need to set the equation to zero by moving all terms to one side of the equation. $\newline$ $-2x^2 + 7x - 1 - (-3x^2 + 14) = 0$
Simplify Equation: Simplify the equation by combining like terms. $-2x^2 + 7x - 1 + 3x^2 - 14 = 0$
Combine Terms: Combine the $x^2$ terms and the constant terms. $\newline$ $(3x^2 - 2x^2) + 7x - (14 + 1) = 0$ $\newline$ $x^2 + 7x - 15 = 0$
Solve Quadratic Equation: Now we need to solve the quadratic equation $x^2 + 7x - 15 = 0$ . We can use the quadratic formula, where $a = 1$ , $b = 7$ , and $c = -15$ . $\newline$ $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute Values: Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula. $x = \frac{-7 \pm \sqrt{7^2 - 4(1)(-15)}}{2(1)}$
Calculate Discriminant: Calculate the discriminant (the part under the square root). Discriminant = $7^2 - 4(1)(-15) = 49 + 60 = 109$
Substitute Discriminant: Substitute the discriminant back into the quadratic formula. $x = \frac{-7 \pm \sqrt{109}}{2}$
Calculate Solutions: Calculate the two possible solutions for $x$ . $x = \frac{{-7 + \sqrt{109}}}{{2}}$ or $x = \frac{{-7 - \sqrt{109}}}{{2}}$
Find Numerical Values: Use a calculator to find the numerical values of $x$ to the nearest tenth.x \approx (\-7 + 10.4) / 2 or x \approx (\-7 - 10.4) / 2 $x \approx 1.7$ or $x \approx -8.7$