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Simplifying x + -1x2 = 0.14959 Solving x + -1x2 = 0.14959 Solving for variable 'x'. Reorder the terms: -0.14959 + x + -1x2 = 0.14959 + -0.14959 Combine like terms: 0.14959 + -0.14959 = 0.00000 -0.14959 + x + -1x2 = 0.00000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.14959 + -1x + x2 = 0.00000 Move the constant term to the right: Add '-0.14959' to each side of the equation. 0.14959 + -1x + -0.14959 + x2 = 0.00000 + -0.14959 Reorder the terms: 0.14959 + -0.14959 + -1x + x2 = 0.00000 + -0.14959 Combine like terms: 0.14959 + -0.14959 = 0.00000 0.00000 + -1x + x2 = 0.00000 + -0.14959 -1x + x2 = 0.00000 + -0.14959 Combine like terms: 0.00000 + -0.14959 = -0.14959 -1x + x2 = -0.14959 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.14959 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.14959 + 0.25 Combine like terms: -0.14959 + 0.25 = 0.10041 0.25 + -1x + x2 = 0.10041 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.10041 Calculate the square root of the right side: 0.31687537 Break this problem into two subproblems by setting (x + 0.5) equal to 0.31687537 and -0.31687537.Subproblem 1
x + 0.5 = 0.31687537 Simplifying x + 0.5 = 0.31687537 Reorder the terms: 0.5 + x = 0.31687537 Solving 0.5 + x = 0.31687537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.31687537 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.31687537 + -0.5 x = 0.31687537 + -0.5 Combine like terms: 0.31687537 + -0.5 = -0.18312463 x = -0.18312463 Simplifying x = -0.18312463Subproblem 2
x + 0.5 = -0.31687537 Simplifying x + 0.5 = -0.31687537 Reorder the terms: 0.5 + x = -0.31687537 Solving 0.5 + x = -0.31687537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.31687537 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.31687537 + -0.5 x = -0.31687537 + -0.5 Combine like terms: -0.31687537 + -0.5 = -0.81687537 x = -0.81687537 Simplifying x = -0.81687537Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.18312463, -0.81687537}
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