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Simplifying 32x2 + -8x + -15 = 0 Reorder the terms: -15 + -8x + 32x2 = 0 Solving -15 + -8x + 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'. -0.46875 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.46875' to each side of the equation. -0.46875 + -0.25x + 0.46875 + x2 = 0 + 0.46875 Reorder the terms: -0.46875 + 0.46875 + -0.25x + x2 = 0 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + -0.25x + x2 = 0 + 0.46875 -0.25x + x2 = 0 + 0.46875 Combine like terms: 0 + 0.46875 = 0.46875 -0.25x + x2 = 0.46875 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.46875 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.46875 + 0.015625 Combine like terms: 0.46875 + 0.015625 = 0.484375 0.015625 + -0.25x + x2 = 0.484375 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.484375 Calculate the square root of the right side: 0.695970545 Break this problem into two subproblems by setting (x + -0.125) equal to 0.695970545 and -0.695970545.Subproblem 1
x + -0.125 = 0.695970545 Simplifying x + -0.125 = 0.695970545 Reorder the terms: -0.125 + x = 0.695970545 Solving -0.125 + x = 0.695970545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.695970545 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.695970545 + 0.125 x = 0.695970545 + 0.125 Combine like terms: 0.695970545 + 0.125 = 0.820970545 x = 0.820970545 Simplifying x = 0.820970545Subproblem 2
x + -0.125 = -0.695970545 Simplifying x + -0.125 = -0.695970545 Reorder the terms: -0.125 + x = -0.695970545 Solving -0.125 + x = -0.695970545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.695970545 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.695970545 + 0.125 x = -0.695970545 + 0.125 Combine like terms: -0.695970545 + 0.125 = -0.570970545 x = -0.570970545 Simplifying x = -0.570970545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.820970545, -0.570970545}
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