Solve. 6-6x^(2)-3x=0 Choose 1 answer: (A) x=(7+-sqrt193)/(-12) (B) x=(5+-sqrt57)/(16) (C) x=(1+-sqrt17)/(-4) (D) x=(-4+-sqrt34)/(3)

Question

Solve.  6-6x^(2)-3x=0 Choose 1 answer: (A)  x=(7+-sqrt193)/(-12) (B)  x=(5+-sqrt57)/(16) (C)  x=(1+-sqrt17)/(-4) (D)  x=(-4+-sqrt34)/(3)

Bytelearn · Accepted Answer

Identify coefficients of quadratic equation: Identify the coefficients of the quadratic equation. The quadratic equation is given by 6 - 6x^2 - 3x = 0. To compare it with the standard form ax^2 + bx + c = 0, we need to rearrange the terms to get -6x^2 - 3x + 6 = 0. Now we can identify the coefficients: a = -6, b = -3, and c = 6.Apply quadratic formula: Apply the quadratic formula to find the solutions for x. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a). We will substitute a = -6, b = -3, and c = 6 into the formula.Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. The discriminant is (-3)^2 - 4(-6)(6) = 9 - (-144) = 9 + 144 = 153.Substitute values into quadratic formula: Substitute the values of a, b, and the discriminant into the quadratic formula. x = (-(-3) ± sqrt(153)) / (2(-6)) x = (3 ± sqrt(153)) / (-12)Simplify solutions: Simplify the solutions. Since sqrt(153) cannot be simplified to an integer or a simple fraction, we leave it as is. The two possible solutions for x are: x = (3 + sqrt(153)) / (-12) or x = (3 - sqrt(153)) / (-12)Match solutions with answer choices: Match the solutions with the given answer choices. The solutions we found are x = (3 + sqrt(153)) / (-12) or x = (3 - sqrt(153)) / (-12). We need to find which answer choice corresponds to these solutions. By looking at the answer choices, we can see that the correct answer is: (A) x = (7 ± sqrt(193)) / (-12) (B) x = (5 ± sqrt(57)) / (16) (C) x = (1 ± sqrt(17)) / (-4) (D) x = (-4 ± sqrt(34)) / (3) None of these match our solutions exactly, so we must have made a mistake.

Solve. $\newline$ $6-6x^{2}-3x=0$ $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $x=\frac{7\pm\sqrt{193}}{-12}$ $\newline$ (B) $\newline$ $x=\frac{5\pm\sqrt{57}}{16}$ $\newline$ (C) $\newline$ $x=\frac{1\pm\sqrt{17}}{-4}$ $\newline$ (D) $\newline$ $x=\frac{-4\pm\sqrt{34}}{3}$

Full solution

More problems from Solve a quadratic equation using the quadratic formula

Related topics