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Simplifying 20x = (x + 6)(20 + -1x + -1) Reorder the terms: 20x = (6 + x)(20 + -1x + -1) Reorder the terms: 20x = (6 + x)(20 + -1 + -1x) Combine like terms: 20 + -1 = 19 20x = (6 + x)(19 + -1x) Multiply (6 + x) * (19 + -1x) 20x = (6(19 + -1x) + x(19 + -1x)) 20x = ((19 * 6 + -1x * 6) + x(19 + -1x)) 20x = ((114 + -6x) + x(19 + -1x)) 20x = (114 + -6x + (19 * x + -1x * x)) 20x = (114 + -6x + (19x + -1x2)) Combine like terms: -6x + 19x = 13x 20x = (114 + 13x + -1x2) Solving 20x = 114 + 13x + -1x2 Solving for variable 'x'. Reorder the terms: -114 + 20x + -13x + x2 = 114 + 13x + -1x2 + -114 + -13x + x2 Combine like terms: 20x + -13x = 7x -114 + 7x + x2 = 114 + 13x + -1x2 + -114 + -13x + x2 Reorder the terms: -114 + 7x + x2 = 114 + -114 + 13x + -13x + -1x2 + x2 Combine like terms: 114 + -114 = 0 -114 + 7x + x2 = 0 + 13x + -13x + -1x2 + x2 -114 + 7x + x2 = 13x + -13x + -1x2 + x2 Combine like terms: 13x + -13x = 0 -114 + 7x + x2 = 0 + -1x2 + x2 -114 + 7x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -114 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + 7x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + 7x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + 7x + x2 = 0 + 114 7x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 7x + x2 = 114 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 114 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 114 + 12.25 Combine like terms: 114 + 12.25 = 126.25 12.25 + 7x + x2 = 126.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + 3.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + 3.5 = 11.236102527 Simplifying x + 3.5 = 11.236102527 Reorder the terms: 3.5 + x = 11.236102527 Solving 3.5 + x = 11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 11.236102527 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.236102527 + -3.5 x = 11.236102527 + -3.5 Combine like terms: 11.236102527 + -3.5 = 7.736102527 x = 7.736102527 Simplifying x = 7.736102527Subproblem 2
x + 3.5 = -11.236102527 Simplifying x + 3.5 = -11.236102527 Reorder the terms: 3.5 + x = -11.236102527 Solving 3.5 + x = -11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -11.236102527 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.236102527 + -3.5 x = -11.236102527 + -3.5 Combine like terms: -11.236102527 + -3.5 = -14.736102527 x = -14.736102527 Simplifying x = -14.736102527Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.736102527, -14.736102527}
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