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Simplifying 6x2 + -24x + -765 = 0 Reorder the terms: -765 + -24x + 6x2 = 0 Solving -765 + -24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-255 + -8x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-255 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying -255 + -8x + 2x2 = 0 Solving -255 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -127.5 + -4x + x2 = 0 Move the constant term to the right: Add '127.5' to each side of the equation. -127.5 + -4x + 127.5 + x2 = 0 + 127.5 Reorder the terms: -127.5 + 127.5 + -4x + x2 = 0 + 127.5 Combine like terms: -127.5 + 127.5 = 0.0 0.0 + -4x + x2 = 0 + 127.5 -4x + x2 = 0 + 127.5 Combine like terms: 0 + 127.5 = 127.5 -4x + x2 = 127.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 127.5 + 4 Reorder the terms: 4 + -4x + x2 = 127.5 + 4 Combine like terms: 127.5 + 4 = 131.5 4 + -4x + x2 = 131.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 131.5 Calculate the square root of the right side: 11.467344941 Break this problem into two subproblems by setting (x + -2) equal to 11.467344941 and -11.467344941.Subproblem 1
x + -2 = 11.467344941 Simplifying x + -2 = 11.467344941 Reorder the terms: -2 + x = 11.467344941 Solving -2 + x = 11.467344941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 11.467344941 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.467344941 + 2 x = 11.467344941 + 2 Combine like terms: 11.467344941 + 2 = 13.467344941 x = 13.467344941 Simplifying x = 13.467344941Subproblem 2
x + -2 = -11.467344941 Simplifying x + -2 = -11.467344941 Reorder the terms: -2 + x = -11.467344941 Solving -2 + x = -11.467344941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -11.467344941 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.467344941 + 2 x = -11.467344941 + 2 Combine like terms: -11.467344941 + 2 = -9.467344941 x = -9.467344941 Simplifying x = -9.467344941Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.467344941, -9.467344941}Solution
x = {13.467344941, -9.467344941}
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