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Simplifying -16x2 + -12x + 15 = 0 Reorder the terms: 15 + -12x + -16x2 = 0 Solving 15 + -12x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.9375 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 0.75x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 0.75x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 0.75x + x2 = 0 + 0.9375 0.75x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 0.75x + x2 = 0.9375 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 = 0.9375 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.9375 + 0.140625 Combine like terms: 0.9375 + 0.140625 = 1.078125 0.140625 + 0.75x + x2 = 1.078125 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.078125 Calculate the square root of the right side: 1.038327983 Break this problem into two subproblems by setting (x + 0.375) equal to 1.038327983 and -1.038327983.Subproblem 1
x + 0.375 = 1.038327983 Simplifying x + 0.375 = 1.038327983 Reorder the terms: 0.375 + x = 1.038327983 Solving 0.375 + x = 1.038327983 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 = 1.038327983 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.038327983 + -0.375 x = 1.038327983 + -0.375 Combine like terms: 1.038327983 + -0.375 = 0.663327983 x = 0.663327983 Simplifying x = 0.663327983Subproblem 2
x + 0.375 = -1.038327983 Simplifying x + 0.375 = -1.038327983 Reorder the terms: 0.375 + x = -1.038327983 Solving 0.375 + x = -1.038327983 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 = -1.038327983 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.038327983 + -0.375 x = -1.038327983 + -0.375 Combine like terms: -1.038327983 + -0.375 = -1.413327983 x = -1.413327983 Simplifying x = -1.413327983Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.663327983, -1.413327983}
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