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Simplifying 16x2 + -10x + -15 = 0 Reorder the terms: -15 + -10x + 16x2 = 0 Solving -15 + -10x + 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 + -0.625x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -0.625x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -0.625x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -0.625x + x2 = 0 + 0.9375 -0.625x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -0.625x + x2 = 0.9375 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 0.9375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 0.9375 + 0.09765625 Combine like terms: 0.9375 + 0.09765625 = 1.03515625 0.09765625 + -0.625x + x2 = 1.03515625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 1.03515625 Calculate the square root of the right side: 1.017426287 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.017426287 and -1.017426287.Subproblem 1
x + -0.3125 = 1.017426287 Simplifying x + -0.3125 = 1.017426287 Reorder the terms: -0.3125 + x = 1.017426287 Solving -0.3125 + x = 1.017426287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.017426287 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.017426287 + 0.3125 x = 1.017426287 + 0.3125 Combine like terms: 1.017426287 + 0.3125 = 1.329926287 x = 1.329926287 Simplifying x = 1.329926287Subproblem 2
x + -0.3125 = -1.017426287 Simplifying x + -0.3125 = -1.017426287 Reorder the terms: -0.3125 + x = -1.017426287 Solving -0.3125 + x = -1.017426287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.017426287 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.017426287 + 0.3125 x = -1.017426287 + 0.3125 Combine like terms: -1.017426287 + 0.3125 = -0.704926287 x = -0.704926287 Simplifying x = -0.704926287Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.329926287, -0.704926287}
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