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Simplifying 32x2 + 15x + -3 = 0 Reorder the terms: -3 + 15x + 32x2 = 0 Solving -3 + 15x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.09375 + 0.46875x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + 0.46875x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + 0.46875x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + 0.46875x + x2 = 0 + 0.09375 0.46875x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 0.46875x + x2 = 0.09375 The x term is 0.46875x. Take half its coefficient (0.234375). Square it (0.05493164063) and add it to both sides. Add '0.05493164063' to each side of the equation. 0.46875x + 0.05493164063 + x2 = 0.09375 + 0.05493164063 Reorder the terms: 0.05493164063 + 0.46875x + x2 = 0.09375 + 0.05493164063 Combine like terms: 0.09375 + 0.05493164063 = 0.14868164063 0.05493164063 + 0.46875x + x2 = 0.14868164063 Factor a perfect square on the left side: (x + 0.234375)(x + 0.234375) = 0.14868164063 Calculate the square root of the right side: 0.385592584 Break this problem into two subproblems by setting (x + 0.234375) equal to 0.385592584 and -0.385592584.Subproblem 1
x + 0.234375 = 0.385592584 Simplifying x + 0.234375 = 0.385592584 Reorder the terms: 0.234375 + x = 0.385592584 Solving 0.234375 + x = 0.385592584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.234375' to each side of the equation. 0.234375 + -0.234375 + x = 0.385592584 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + x = 0.385592584 + -0.234375 x = 0.385592584 + -0.234375 Combine like terms: 0.385592584 + -0.234375 = 0.151217584 x = 0.151217584 Simplifying x = 0.151217584Subproblem 2
x + 0.234375 = -0.385592584 Simplifying x + 0.234375 = -0.385592584 Reorder the terms: 0.234375 + x = -0.385592584 Solving 0.234375 + x = -0.385592584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.234375' to each side of the equation. 0.234375 + -0.234375 + x = -0.385592584 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + x = -0.385592584 + -0.234375 x = -0.385592584 + -0.234375 Combine like terms: -0.385592584 + -0.234375 = -0.619967584 x = -0.619967584 Simplifying x = -0.619967584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.151217584, -0.619967584}
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