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Simplifying 18x + -5 = 3x(6x + -2) Reorder the terms: -5 + 18x = 3x(6x + -2) Reorder the terms: -5 + 18x = 3x(-2 + 6x) -5 + 18x = (-2 * 3x + 6x * 3x) -5 + 18x = (-6x + 18x2) Solving -5 + 18x = -6x + 18x2 Solving for variable 'x'. Combine like terms: 18x + 6x = 24x -5 + 24x + -18x2 = -6x + 18x2 + 6x + -18x2 Reorder the terms: -5 + 24x + -18x2 = -6x + 6x + 18x2 + -18x2 Combine like terms: -6x + 6x = 0 -5 + 24x + -18x2 = 0 + 18x2 + -18x2 -5 + 24x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -5 + 24x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 0.2777777778 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + -1.333333333x + -0.2777777778 + x2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + -1.333333333x + x2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + -0.2777777778 -1.333333333x + x2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 -1.333333333x + x2 = -0.2777777778 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -0.2777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.2777777778 + 0.4444444442 Combine like terms: -0.2777777778 + 0.4444444442 = 0.1666666664 0.4444444442 + -1.333333333x + x2 = 0.1666666664 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.1666666664 Calculate the square root of the right side: 0.40824829 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.40824829 and -0.40824829.Subproblem 1
x + -0.6666666665 = 0.40824829 Simplifying x + -0.6666666665 = 0.40824829 Reorder the terms: -0.6666666665 + x = 0.40824829 Solving -0.6666666665 + x = 0.40824829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.40824829 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.40824829 + 0.6666666665 x = 0.40824829 + 0.6666666665 Combine like terms: 0.40824829 + 0.6666666665 = 1.0749149565 x = 1.0749149565 Simplifying x = 1.0749149565Subproblem 2
x + -0.6666666665 = -0.40824829 Simplifying x + -0.6666666665 = -0.40824829 Reorder the terms: -0.6666666665 + x = -0.40824829 Solving -0.6666666665 + x = -0.40824829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.40824829 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.40824829 + 0.6666666665 x = -0.40824829 + 0.6666666665 Combine like terms: -0.40824829 + 0.6666666665 = 0.2584183765 x = 0.2584183765 Simplifying x = 0.2584183765Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0749149565, 0.2584183765}
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