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Simplifying x[6 + -1(-3x + -1)] = 54x + 72 Reorder the terms: x[6 + -1(-1 + -3x)] = 54x + 72 x[6 + (-1 * -1 + -3x * -1)] = 54x + 72 x[6 + (1 + 3x)] = 54x + 72 Combine like terms: 6 + 1 = 7 x[7 + 3x] = 54x + 72 [7 * x + 3x * x] = 54x + 72 [7x + 3x2] = 54x + 72 Reorder the terms: 7x + 3x2 = 72 + 54x Solving 7x + 3x2 = 72 + 54x Solving for variable 'x'. Reorder the terms: -72 + 7x + -54x + 3x2 = 72 + 54x + -72 + -54x Combine like terms: 7x + -54x = -47x -72 + -47x + 3x2 = 72 + 54x + -72 + -54x Reorder the terms: -72 + -47x + 3x2 = 72 + -72 + 54x + -54x Combine like terms: 72 + -72 = 0 -72 + -47x + 3x2 = 0 + 54x + -54x -72 + -47x + 3x2 = 54x + -54x Combine like terms: 54x + -54x = 0 -72 + -47x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24 + -15.66666667x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -15.66666667x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -15.66666667x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -15.66666667x + x2 = 0 + 24 -15.66666667x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -15.66666667x + x2 = 24 The x term is -15.66666667x. Take half its coefficient (-7.833333335). Square it (61.36111114) and add it to both sides. Add '61.36111114' to each side of the equation. -15.66666667x + 61.36111114 + x2 = 24 + 61.36111114 Reorder the terms: 61.36111114 + -15.66666667x + x2 = 24 + 61.36111114 Combine like terms: 24 + 61.36111114 = 85.36111114 61.36111114 + -15.66666667x + x2 = 85.36111114 Factor a perfect square on the left side: (x + -7.833333335)(x + -7.833333335) = 85.36111114 Calculate the square root of the right side: 9.239107703 Break this problem into two subproblems by setting (x + -7.833333335) equal to 9.239107703 and -9.239107703.Subproblem 1
x + -7.833333335 = 9.239107703 Simplifying x + -7.833333335 = 9.239107703 Reorder the terms: -7.833333335 + x = 9.239107703 Solving -7.833333335 + x = 9.239107703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.833333335' to each side of the equation. -7.833333335 + 7.833333335 + x = 9.239107703 + 7.833333335 Combine like terms: -7.833333335 + 7.833333335 = 0.000000000 0.000000000 + x = 9.239107703 + 7.833333335 x = 9.239107703 + 7.833333335 Combine like terms: 9.239107703 + 7.833333335 = 17.072441038 x = 17.072441038 Simplifying x = 17.072441038Subproblem 2
x + -7.833333335 = -9.239107703 Simplifying x + -7.833333335 = -9.239107703 Reorder the terms: -7.833333335 + x = -9.239107703 Solving -7.833333335 + x = -9.239107703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.833333335' to each side of the equation. -7.833333335 + 7.833333335 + x = -9.239107703 + 7.833333335 Combine like terms: -7.833333335 + 7.833333335 = 0.000000000 0.000000000 + x = -9.239107703 + 7.833333335 x = -9.239107703 + 7.833333335 Combine like terms: -9.239107703 + 7.833333335 = -1.405774368 x = -1.405774368 Simplifying x = -1.405774368Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.072441038, -1.405774368}
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