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Simplifying 6x2 + 32x + -2640 = 0 Reorder the terms: -2640 + 32x + 6x2 = 0 Solving -2640 + 32x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1320 + 16x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1320 + 16x + 3x2)' equal to zero and attempt to solve: Simplifying -1320 + 16x + 3x2 = 0 Solving -1320 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -440 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '440' to each side of the equation. -440 + 5.333333333x + 440 + x2 = 0 + 440 Reorder the terms: -440 + 440 + 5.333333333x + x2 = 0 + 440 Combine like terms: -440 + 440 = 0 0 + 5.333333333x + x2 = 0 + 440 5.333333333x + x2 = 0 + 440 Combine like terms: 0 + 440 = 440 5.333333333x + x2 = 440 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 440 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 440 + 7.111111113 Combine like terms: 440 + 7.111111113 = 447.111111113 7.111111113 + 5.333333333x + x2 = 447.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 447.111111113 Calculate the square root of the right side: 21.145002036 Break this problem into two subproblems by setting (x + 2.666666667) equal to 21.145002036 and -21.145002036.Subproblem 1
x + 2.666666667 = 21.145002036 Simplifying x + 2.666666667 = 21.145002036 Reorder the terms: 2.666666667 + x = 21.145002036 Solving 2.666666667 + x = 21.145002036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 21.145002036 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 21.145002036 + -2.666666667 x = 21.145002036 + -2.666666667 Combine like terms: 21.145002036 + -2.666666667 = 18.478335369 x = 18.478335369 Simplifying x = 18.478335369Subproblem 2
x + 2.666666667 = -21.145002036 Simplifying x + 2.666666667 = -21.145002036 Reorder the terms: 2.666666667 + x = -21.145002036 Solving 2.666666667 + x = -21.145002036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -21.145002036 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -21.145002036 + -2.666666667 x = -21.145002036 + -2.666666667 Combine like terms: -21.145002036 + -2.666666667 = -23.811668703 x = -23.811668703 Simplifying x = -23.811668703Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.478335369, -23.811668703}Solution
x = {18.478335369, -23.811668703}
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