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Simplifying 16x2 + 14x + -15 = 10 Reorder the terms: -15 + 14x + 16x2 = 10 Solving -15 + 14x + 16x2 = 10 Solving for variable 'x'. Reorder the terms: -15 + -10 + 14x + 16x2 = 10 + -10 Combine like terms: -15 + -10 = -25 -25 + 14x + 16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -25 + 14x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + 0.875x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.875x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.875x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.875x + x2 = 0 + 1.5625 0.875x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.875x + x2 = 1.5625 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 1.5625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 1.5625 + 0.19140625 Combine like terms: 1.5625 + 0.19140625 = 1.75390625 0.19140625 + 0.875x + x2 = 1.75390625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 1.75390625 Calculate the square root of the right side: 1.324351256 Break this problem into two subproblems by setting (x + 0.4375) equal to 1.324351256 and -1.324351256.Subproblem 1
x + 0.4375 = 1.324351256 Simplifying x + 0.4375 = 1.324351256 Reorder the terms: 0.4375 + x = 1.324351256 Solving 0.4375 + x = 1.324351256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 1.324351256 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 1.324351256 + -0.4375 x = 1.324351256 + -0.4375 Combine like terms: 1.324351256 + -0.4375 = 0.886851256 x = 0.886851256 Simplifying x = 0.886851256Subproblem 2
x + 0.4375 = -1.324351256 Simplifying x + 0.4375 = -1.324351256 Reorder the terms: 0.4375 + x = -1.324351256 Solving 0.4375 + x = -1.324351256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -1.324351256 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -1.324351256 + -0.4375 x = -1.324351256 + -0.4375 Combine like terms: -1.324351256 + -0.4375 = -1.761851256 x = -1.761851256 Simplifying x = -1.761851256Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.886851256, -1.761851256}
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