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Simplifying x2 + -1x + 0.25 = 15.93945 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 15.93945 + 0.25 Combine like terms: 15.93945 + 0.25 = 16.18945 0.25 + -1x + x2 = 16.18945 Solving 0.25 + -1x + x2 = 16.18945 Solving for variable 'x'. Reorder the terms: 0.25 + -16.18945 + -1x + x2 = 16.18945 + -16.18945 Combine like terms: 0.25 + -16.18945 = -15.93945 -15.93945 + -1x + x2 = 16.18945 + -16.18945 Combine like terms: 16.18945 + -16.18945 = 0.00000 -15.93945 + -1x + x2 = 0.00000 Begin completing the square. Move the constant term to the right: Add '15.93945' to each side of the equation. -15.93945 + -1x + 15.93945 + x2 = 0.00000 + 15.93945 Reorder the terms: -15.93945 + 15.93945 + -1x + x2 = 0.00000 + 15.93945 Combine like terms: -15.93945 + 15.93945 = 0.00000 0.00000 + -1x + x2 = 0.00000 + 15.93945 -1x + x2 = 0.00000 + 15.93945 Combine like terms: 0.00000 + 15.93945 = 15.93945 -1x + x2 = 15.93945 The x term is -1x. 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 = 15.93945 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 15.93945 + 0.25 Combine like terms: 15.93945 + 0.25 = 16.18945 0.25 + -1x + x2 = 16.18945 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 16.18945 Calculate the square root of the right side: 4.023611562 Break this problem into two subproblems by setting (x + -0.5) equal to 4.023611562 and -4.023611562.Subproblem 1
x + -0.5 = 4.023611562 Simplifying x + -0.5 = 4.023611562 Reorder the terms: -0.5 + x = 4.023611562 Solving -0.5 + x = 4.023611562 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 = 4.023611562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.023611562 + 0.5 x = 4.023611562 + 0.5 Combine like terms: 4.023611562 + 0.5 = 4.523611562 x = 4.523611562 Simplifying x = 4.523611562Subproblem 2
x + -0.5 = -4.023611562 Simplifying x + -0.5 = -4.023611562 Reorder the terms: -0.5 + x = -4.023611562 Solving -0.5 + x = -4.023611562 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 = -4.023611562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.023611562 + 0.5 x = -4.023611562 + 0.5 Combine like terms: -4.023611562 + 0.5 = -3.523611562 x = -3.523611562 Simplifying x = -3.523611562Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.523611562, -3.523611562}
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