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Simplifying 12.5x2 + 13.2x = 15.5 Reorder the terms: 13.2x + 12.5x2 = 15.5 Solving 13.2x + 12.5x2 = 15.5 Solving for variable 'x'. Reorder the terms: -15.5 + 13.2x + 12.5x2 = 15.5 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 -15.5 + 13.2x + 12.5x2 = 0.0 Begin completing the square. Divide all terms by 12.5 the coefficient of the squared term: Divide each side by '12.5'. -1.24 + 1.056x + x2 = 0 Move the constant term to the right: Add '1.24' to each side of the equation. -1.24 + 1.056x + 1.24 + x2 = 0 + 1.24 Reorder the terms: -1.24 + 1.24 + 1.056x + x2 = 0 + 1.24 Combine like terms: -1.24 + 1.24 = 0.00 0.00 + 1.056x + x2 = 0 + 1.24 1.056x + x2 = 0 + 1.24 Combine like terms: 0 + 1.24 = 1.24 1.056x + x2 = 1.24 The x term is 1.056x. Take half its coefficient (0.528). Square it (0.278784) and add it to both sides. Add '0.278784' to each side of the equation. 1.056x + 0.278784 + x2 = 1.24 + 0.278784 Reorder the terms: 0.278784 + 1.056x + x2 = 1.24 + 0.278784 Combine like terms: 1.24 + 0.278784 = 1.518784 0.278784 + 1.056x + x2 = 1.518784 Factor a perfect square on the left side: (x + 0.528)(x + 0.528) = 1.518784 Calculate the square root of the right side: 1.232389549 Break this problem into two subproblems by setting (x + 0.528) equal to 1.232389549 and -1.232389549.Subproblem 1
x + 0.528 = 1.232389549 Simplifying x + 0.528 = 1.232389549 Reorder the terms: 0.528 + x = 1.232389549 Solving 0.528 + x = 1.232389549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.528' to each side of the equation. 0.528 + -0.528 + x = 1.232389549 + -0.528 Combine like terms: 0.528 + -0.528 = 0.000 0.000 + x = 1.232389549 + -0.528 x = 1.232389549 + -0.528 Combine like terms: 1.232389549 + -0.528 = 0.704389549 x = 0.704389549 Simplifying x = 0.704389549Subproblem 2
x + 0.528 = -1.232389549 Simplifying x + 0.528 = -1.232389549 Reorder the terms: 0.528 + x = -1.232389549 Solving 0.528 + x = -1.232389549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.528' to each side of the equation. 0.528 + -0.528 + x = -1.232389549 + -0.528 Combine like terms: 0.528 + -0.528 = 0.000 0.000 + x = -1.232389549 + -0.528 x = -1.232389549 + -0.528 Combine like terms: -1.232389549 + -0.528 = -1.760389549 x = -1.760389549 Simplifying x = -1.760389549Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.704389549, -1.760389549}
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