Solve. -6+3x-9x^(2)=-16 Choose 1 answer: (A) x=(7+-sqrt77)/(2) (B) x=(-5+-sqrt305)/(14) (C) x=(-1+-2sqrt2)/(-7) (D) x=(-1+-sqrt41)/(-6)

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Solve.  -6+3x-9x^(2)=-16 Choose 1 answer: (A)  x=(7+-sqrt77)/(2) (B)  x=(-5+-sqrt305)/(14) (C)  x=(-1+-2sqrt2)/(-7) (D)  x=(-1+-sqrt41)/(-6)

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Write equation in standard form: Write the equation in standard form. To solve the quadratic equation, we first need to write it in the standard form ax^2 + bx + c = 0. We have the equation -6 + 3x - 9x^2 = -16. Let's move all terms to one side to get it in standard form. -9x^2 + 3x - 6 = -16 Now, add 16 to both sides of the equation. -9x^2 + 3x - 6 + 16 = 0 -9x^2 + 3x + 10 = 0Identify values of a, b, and c: Identify the values of a, b, and c. Now that we have the equation in standard form, we can identify the coefficients a, b, and c, which we will use in the quadratic formula. a = -9 b = 3 c = 10Substitute values into quadratic formula: Substitute the values into the quadratic formula. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Let's substitute the values of a, b, and c into the formula. x = (-(3) ± sqrt((3)^2 - 4(-9)(10))) / (2(-9)) x = (-3 ± sqrt(9 + 360)) / (-18)Simplify under square root and solve for x: Simplify under the square root and solve for x. Now we simplify the expression under the square root and then find the values of x. x = (-3 ± sqrt(369)) / (-18) We cannot simplify sqrt(369) further, so we will use this value as it is.Find two possible solutions for x: Find the two possible solutions for x. We have two possible solutions for x, corresponding to the '±' in the quadratic formula. x = (-3 + sqrt(369)) / (-18) or x = (-3 - sqrt(369)) / (-18)Simplify the solutions: Simplify the solutions. We can simplify the solutions by dividing both numerator and denominator by -3 to make the denominator positive. x = (1 - sqrt(369)) / 6 or x = (1 + sqrt(369)) / 6Check the answer choices: Check the answer choices. Now we compare our solutions with the given answer choices. (A) x = (7 ± sqrt(77)) / 2 (B) x = (-5 ± sqrt(305)) / 14 (C) x = (-1 ± 2sqrt(2)) / (-7) (D) x = (-1 ± sqrt(41)) / (-6) None of these match our solutions exactly, but we can see that answer choice (D) is the closest in form to our solutions. However, the numbers do not match, so there seems to be a mistake.

Solve. $\newline$ $-6+3 x-9 x^{2}=-16$ $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{7 \pm \sqrt{77}}{2}$ $\newline$ (B) $x=\frac{-5 \pm \sqrt{305}}{14}$ $\newline$ (C) $x=\frac{-1 \pm 2 \sqrt{2}}{-7}$ $\newline$ (D) $x=\frac{-1 \pm \sqrt{41}}{-6}$

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