x=(-5+-sqrt((5)^(2)-4(1)(6)))/(2(1))

Identify Quadratic Equation: We are asked to solve the quadratic equation using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). In this case, the quadratic equation is already in the form of the quadratic formula, where a = 1, b = -5, and c = -66 (since -4 * 11 * 6 = -264).Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b² - 4ac. Discriminant = (5)² - 4(1)(-66) = 25 + 264 = 289.Find Square Root: Next, we take the square root of the discriminant: √289. √289 = 17.Apply Quadratic Formula: Now we can use the quadratic formula to find the two possible values for x. x = (-(-5) ± 17) / (2 * 1) = (5 ± 17) / 2.Calculate First Solution: We have two solutions for x, one using the plus sign and one using the minus sign. First solution: x = (5 + 17) / 2 = 22 / 2 = 11. Second solution: x = (5 - 17) / 2 = -12 / 2 = -6.Calculate Second Solution: We have found the two values of x that satisfy the quadratic equation.

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x=\frac{-5 \pm \sqrt{(5)^{2}-4(1)(6)}}{2(1)}

Identify Quadratic Equation: We are asked to solve the quadratic equation using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . In this case, the quadratic equation is already in the form of the quadratic formula, where $a = 1$ , $b = -5$ , and $c = -66$ (since $-4 \times 11 \times 6 = -264$ ).
Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . Discriminant = $(5)^2 - 4(1)(-66) = 25 + 264 = 289$ .
Find Square Root: Next, we take the square root of the discriminant: $\sqrt{289}$ . $\sqrt{289} = 17$ .
Apply Quadratic Formula: Now we can use the quadratic formula to find the two possible values for $x$ . $x = \frac{-(-5) \pm \sqrt{17}}{2 \times 1} = \frac{5 \pm \sqrt{17}}{2}$ .
Calculate First Solution: We have two solutions for $x$ , one using the plus sign and one using the minus sign. $\newline$ First solution: $x = (5 + 17) / 2 = 22 / 2 = 11$ . $\newline$ Second solution: $x = (5 - 17) / 2 = -12 / 2 = -6$ .
Calculate Second Solution: We have found the two values of $x$ that satisfy the quadratic equation.