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Simplifying 1x(x + 2) = 6(x + 12) Reorder the terms: 1x(2 + x) = 6(x + 12) (2 * 1x + x * 1x) = 6(x + 12) (2x + 1x2) = 6(x + 12) Reorder the terms: 2x + 1x2 = 6(12 + x) 2x + 1x2 = (12 * 6 + x * 6) 2x + 1x2 = (72 + 6x) Solving 2x + 1x2 = 72 + 6x Solving for variable 'x'. Reorder the terms: -72 + 2x + -6x + 1x2 = 72 + 6x + -72 + -6x Combine like terms: 2x + -6x = -4x -72 + -4x + 1x2 = 72 + 6x + -72 + -6x Reorder the terms: -72 + -4x + 1x2 = 72 + -72 + 6x + -6x Combine like terms: 72 + -72 = 0 -72 + -4x + 1x2 = 0 + 6x + -6x -72 + -4x + 1x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -72 + -4x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -4x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -4x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -4x + x2 = 0 + 72 -4x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -4x + x2 = 72 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 = 72 + 4 Reorder the terms: 4 + -4x + x2 = 72 + 4 Combine like terms: 72 + 4 = 76 4 + -4x + x2 = 76 Factor a perfect square on the left side: (x + -2)(x + -2) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + -2) equal to 8.717797887 and -8.717797887.Subproblem 1
x + -2 = 8.717797887 Simplifying x + -2 = 8.717797887 Reorder the terms: -2 + x = 8.717797887 Solving -2 + x = 8.717797887 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 = 8.717797887 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.717797887 + 2 x = 8.717797887 + 2 Combine like terms: 8.717797887 + 2 = 10.717797887 x = 10.717797887 Simplifying x = 10.717797887Subproblem 2
x + -2 = -8.717797887 Simplifying x + -2 = -8.717797887 Reorder the terms: -2 + x = -8.717797887 Solving -2 + x = -8.717797887 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 = -8.717797887 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.717797887 + 2 x = -8.717797887 + 2 Combine like terms: -8.717797887 + 2 = -6.717797887 x = -6.717797887 Simplifying x = -6.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.717797887, -6.717797887}
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