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Simplifying 88 + x = 3x(x + 22) Reorder the terms: 88 + x = 3x(22 + x) 88 + x = (22 * 3x + x * 3x) 88 + x = (66x + 3x2) Solving 88 + x = 66x + 3x2 Solving for variable 'x'. Combine like terms: x + -66x = -65x 88 + -65x + -3x2 = 66x + 3x2 + -66x + -3x2 Reorder the terms: 88 + -65x + -3x2 = 66x + -66x + 3x2 + -3x2 Combine like terms: 66x + -66x = 0 88 + -65x + -3x2 = 0 + 3x2 + -3x2 88 + -65x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 88 + -65x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -29.33333333 + 21.66666667x + x2 = 0 Move the constant term to the right: Add '29.33333333' to each side of the equation. -29.33333333 + 21.66666667x + 29.33333333 + x2 = 0 + 29.33333333 Reorder the terms: -29.33333333 + 29.33333333 + 21.66666667x + x2 = 0 + 29.33333333 Combine like terms: -29.33333333 + 29.33333333 = 0.00000000 0.00000000 + 21.66666667x + x2 = 0 + 29.33333333 21.66666667x + x2 = 0 + 29.33333333 Combine like terms: 0 + 29.33333333 = 29.33333333 21.66666667x + x2 = 29.33333333 The x term is 21.66666667x. Take half its coefficient (10.83333334). Square it (117.3611113) and add it to both sides. Add '117.3611113' to each side of the equation. 21.66666667x + 117.3611113 + x2 = 29.33333333 + 117.3611113 Reorder the terms: 117.3611113 + 21.66666667x + x2 = 29.33333333 + 117.3611113 Combine like terms: 29.33333333 + 117.3611113 = 146.69444463 117.3611113 + 21.66666667x + x2 = 146.69444463 Factor a perfect square on the left side: (x + 10.83333334)(x + 10.83333334) = 146.69444463 Calculate the square root of the right side: 12.111748207 Break this problem into two subproblems by setting (x + 10.83333334) equal to 12.111748207 and -12.111748207.Subproblem 1
x + 10.83333334 = 12.111748207 Simplifying x + 10.83333334 = 12.111748207 Reorder the terms: 10.83333334 + x = 12.111748207 Solving 10.83333334 + x = 12.111748207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.83333334' to each side of the equation. 10.83333334 + -10.83333334 + x = 12.111748207 + -10.83333334 Combine like terms: 10.83333334 + -10.83333334 = 0.00000000 0.00000000 + x = 12.111748207 + -10.83333334 x = 12.111748207 + -10.83333334 Combine like terms: 12.111748207 + -10.83333334 = 1.278414867 x = 1.278414867 Simplifying x = 1.278414867Subproblem 2
x + 10.83333334 = -12.111748207 Simplifying x + 10.83333334 = -12.111748207 Reorder the terms: 10.83333334 + x = -12.111748207 Solving 10.83333334 + x = -12.111748207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.83333334' to each side of the equation. 10.83333334 + -10.83333334 + x = -12.111748207 + -10.83333334 Combine like terms: 10.83333334 + -10.83333334 = 0.00000000 0.00000000 + x = -12.111748207 + -10.83333334 x = -12.111748207 + -10.83333334 Combine like terms: -12.111748207 + -10.83333334 = -22.945081547 x = -22.945081547 Simplifying x = -22.945081547Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.278414867, -22.945081547}
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