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Simplifying -20x2 + 15x + 64 = 25 Reorder the terms: 64 + 15x + -20x2 = 25 Solving 64 + 15x + -20x2 = 25 Solving for variable 'x'. Reorder the terms: 64 + -25 + 15x + -20x2 = 25 + -25 Combine like terms: 64 + -25 = 39 39 + 15x + -20x2 = 25 + -25 Combine like terms: 25 + -25 = 0 39 + 15x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -1.95 + -0.75x + x2 = 0 Move the constant term to the right: Add '1.95' to each side of the equation. -1.95 + -0.75x + 1.95 + x2 = 0 + 1.95 Reorder the terms: -1.95 + 1.95 + -0.75x + x2 = 0 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + -0.75x + x2 = 0 + 1.95 -0.75x + x2 = 0 + 1.95 Combine like terms: 0 + 1.95 = 1.95 -0.75x + x2 = 1.95 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 1.95 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 1.95 + 0.140625 Combine like terms: 1.95 + 0.140625 = 2.090625 0.140625 + -0.75x + x2 = 2.090625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 2.090625 Calculate the square root of the right side: 1.445899374 Break this problem into two subproblems by setting (x + -0.375) equal to 1.445899374 and -1.445899374.Subproblem 1
x + -0.375 = 1.445899374 Simplifying x + -0.375 = 1.445899374 Reorder the terms: -0.375 + x = 1.445899374 Solving -0.375 + x = 1.445899374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.445899374 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.445899374 + 0.375 x = 1.445899374 + 0.375 Combine like terms: 1.445899374 + 0.375 = 1.820899374 x = 1.820899374 Simplifying x = 1.820899374Subproblem 2
x + -0.375 = -1.445899374 Simplifying x + -0.375 = -1.445899374 Reorder the terms: -0.375 + x = -1.445899374 Solving -0.375 + x = -1.445899374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.445899374 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.445899374 + 0.375 x = -1.445899374 + 0.375 Combine like terms: -1.445899374 + 0.375 = -1.070899374 x = -1.070899374 Simplifying x = -1.070899374Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.820899374, -1.070899374}
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