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Simplifying 32x2 + -15x = 44x + -15 Reorder the terms: -15x + 32x2 = 44x + -15 Reorder the terms: -15x + 32x2 = -15 + 44x Solving -15x + 32x2 = -15 + 44x Solving for variable 'x'. Reorder the terms: 15 + -15x + -44x + 32x2 = -15 + 44x + 15 + -44x Combine like terms: -15x + -44x = -59x 15 + -59x + 32x2 = -15 + 44x + 15 + -44x Reorder the terms: 15 + -59x + 32x2 = -15 + 15 + 44x + -44x Combine like terms: -15 + 15 = 0 15 + -59x + 32x2 = 0 + 44x + -44x 15 + -59x + 32x2 = 44x + -44x Combine like terms: 44x + -44x = 0 15 + -59x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.46875 + -1.84375x + x2 = 0 Move the constant term to the right: Add '-0.46875' to each side of the equation. 0.46875 + -1.84375x + -0.46875 + x2 = 0 + -0.46875 Reorder the terms: 0.46875 + -0.46875 + -1.84375x + x2 = 0 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + -1.84375x + x2 = 0 + -0.46875 -1.84375x + x2 = 0 + -0.46875 Combine like terms: 0 + -0.46875 = -0.46875 -1.84375x + x2 = -0.46875 The x term is -1.84375x. Take half its coefficient (-0.921875). Square it (0.8498535156) and add it to both sides. Add '0.8498535156' to each side of the equation. -1.84375x + 0.8498535156 + x2 = -0.46875 + 0.8498535156 Reorder the terms: 0.8498535156 + -1.84375x + x2 = -0.46875 + 0.8498535156 Combine like terms: -0.46875 + 0.8498535156 = 0.3811035156 0.8498535156 + -1.84375x + x2 = 0.3811035156 Factor a perfect square on the left side: (x + -0.921875)(x + -0.921875) = 0.3811035156 Calculate the square root of the right side: 0.617335821 Break this problem into two subproblems by setting (x + -0.921875) equal to 0.617335821 and -0.617335821.Subproblem 1
x + -0.921875 = 0.617335821 Simplifying x + -0.921875 = 0.617335821 Reorder the terms: -0.921875 + x = 0.617335821 Solving -0.921875 + x = 0.617335821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.921875' to each side of the equation. -0.921875 + 0.921875 + x = 0.617335821 + 0.921875 Combine like terms: -0.921875 + 0.921875 = 0.000000 0.000000 + x = 0.617335821 + 0.921875 x = 0.617335821 + 0.921875 Combine like terms: 0.617335821 + 0.921875 = 1.539210821 x = 1.539210821 Simplifying x = 1.539210821Subproblem 2
x + -0.921875 = -0.617335821 Simplifying x + -0.921875 = -0.617335821 Reorder the terms: -0.921875 + x = -0.617335821 Solving -0.921875 + x = -0.617335821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.921875' to each side of the equation. -0.921875 + 0.921875 + x = -0.617335821 + 0.921875 Combine like terms: -0.921875 + 0.921875 = 0.000000 0.000000 + x = -0.617335821 + 0.921875 x = -0.617335821 + 0.921875 Combine like terms: -0.617335821 + 0.921875 = 0.304539179 x = 0.304539179 Simplifying x = 0.304539179Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.539210821, 0.304539179}
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