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Simplifying 5x + 12x2 = 162 Solving 5x + 12x2 = 162 Solving for variable 'x'. Reorder the terms: -162 + 5x + 12x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -13.5 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 0.4166666667x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 0.4166666667x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 0.4166666667x + x2 = 0 + 13.5 0.4166666667x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 0.4166666667x + x2 = 13.5 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 13.5 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 13.5 + 0.04340277781 Combine like terms: 13.5 + 0.04340277781 = 13.54340277781 0.04340277781 + 0.4166666667x + x2 = 13.54340277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 13.54340277781 Calculate the square root of the right side: 3.680136244 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 3.680136244 and -3.680136244.Subproblem 1
x + 0.2083333334 = 3.680136244 Simplifying x + 0.2083333334 = 3.680136244 Reorder the terms: 0.2083333334 + x = 3.680136244 Solving 0.2083333334 + x = 3.680136244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 3.680136244 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 3.680136244 + -0.2083333334 x = 3.680136244 + -0.2083333334 Combine like terms: 3.680136244 + -0.2083333334 = 3.4718029106 x = 3.4718029106 Simplifying x = 3.4718029106Subproblem 2
x + 0.2083333334 = -3.680136244 Simplifying x + 0.2083333334 = -3.680136244 Reorder the terms: 0.2083333334 + x = -3.680136244 Solving 0.2083333334 + x = -3.680136244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -3.680136244 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -3.680136244 + -0.2083333334 x = -3.680136244 + -0.2083333334 Combine like terms: -3.680136244 + -0.2083333334 = -3.8884695774 x = -3.8884695774 Simplifying x = -3.8884695774Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4718029106, -3.8884695774}
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