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Simplifying 3x(7x + -4) + 6x + -1(13 + -24x2) = 0 Reorder the terms: 3x(-4 + 7x) + 6x + -1(13 + -24x2) = 0 (-4 * 3x + 7x * 3x) + 6x + -1(13 + -24x2) = 0 (-12x + 21x2) + 6x + -1(13 + -24x2) = 0 -12x + 21x2 + 6x + (13 * -1 + -24x2 * -1) = 0 -12x + 21x2 + 6x + (-13 + 24x2) = 0 Reorder the terms: -13 + -12x + 6x + 21x2 + 24x2 = 0 Combine like terms: -12x + 6x = -6x -13 + -6x + 21x2 + 24x2 = 0 Combine like terms: 21x2 + 24x2 = 45x2 -13 + -6x + 45x2 = 0 Solving -13 + -6x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.2888888889 + -0.1333333333x + x2 = 0 Move the constant term to the right: Add '0.2888888889' to each side of the equation. -0.2888888889 + -0.1333333333x + 0.2888888889 + x2 = 0 + 0.2888888889 Reorder the terms: -0.2888888889 + 0.2888888889 + -0.1333333333x + x2 = 0 + 0.2888888889 Combine like terms: -0.2888888889 + 0.2888888889 = 0.0000000000 0.0000000000 + -0.1333333333x + x2 = 0 + 0.2888888889 -0.1333333333x + x2 = 0 + 0.2888888889 Combine like terms: 0 + 0.2888888889 = 0.2888888889 -0.1333333333x + x2 = 0.2888888889 The x term is -0.1333333333x. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333x + 0.004444444442 + x2 = 0.2888888889 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333x + x2 = 0.2888888889 + 0.004444444442 Combine like terms: 0.2888888889 + 0.004444444442 = 0.293333333342 0.004444444442 + -0.1333333333x + x2 = 0.293333333342 Factor a perfect square on the left side: (x + -0.06666666665)(x + -0.06666666665) = 0.293333333342 Calculate the square root of the right side: 0.54160256 Break this problem into two subproblems by setting (x + -0.06666666665) equal to 0.54160256 and -0.54160256.Subproblem 1
x + -0.06666666665 = 0.54160256 Simplifying x + -0.06666666665 = 0.54160256 Reorder the terms: -0.06666666665 + x = 0.54160256 Solving -0.06666666665 + x = 0.54160256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = 0.54160256 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = 0.54160256 + 0.06666666665 x = 0.54160256 + 0.06666666665 Combine like terms: 0.54160256 + 0.06666666665 = 0.60826922665 x = 0.60826922665 Simplifying x = 0.60826922665Subproblem 2
x + -0.06666666665 = -0.54160256 Simplifying x + -0.06666666665 = -0.54160256 Reorder the terms: -0.06666666665 + x = -0.54160256 Solving -0.06666666665 + x = -0.54160256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = -0.54160256 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = -0.54160256 + 0.06666666665 x = -0.54160256 + 0.06666666665 Combine like terms: -0.54160256 + 0.06666666665 = -0.47493589335 x = -0.47493589335 Simplifying x = -0.47493589335Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.60826922665, -0.47493589335}
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