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Simplifying 0 = 0.25 + -1x2 + -2x Reorder the terms: 0 = 0.25 + -2x + -1x2 Solving 0 = 0.25 + -2x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -0.25 = -0.25 -0.25 + 2x + x2 = 0.25 + -2x + -1x2 + -0.25 + 2x + x2 Reorder the terms: -0.25 + 2x + x2 = 0.25 + -0.25 + -2x + 2x + -1x2 + x2 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + 2x + x2 = 0.00 + -2x + 2x + -1x2 + x2 -0.25 + 2x + x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 -0.25 + 2x + x2 = 0 + -1x2 + x2 -0.25 + 2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -0.25 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 2x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 2x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 2x + x2 = 0 + 0.25 2x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 2x + x2 = 0.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.25 + 1 Reorder the terms: 1 + 2x + x2 = 0.25 + 1 Combine like terms: 0.25 + 1 = 1.25 1 + 2x + x2 = 1.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 1) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 1 = 1.118033989 Simplifying x + 1 = 1.118033989 Reorder the terms: 1 + x = 1.118033989 Solving 1 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.118033989 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.118033989 + -1 x = 1.118033989 + -1 Combine like terms: 1.118033989 + -1 = 0.118033989 x = 0.118033989 Simplifying x = 0.118033989Subproblem 2
x + 1 = -1.118033989 Simplifying x + 1 = -1.118033989 Reorder the terms: 1 + x = -1.118033989 Solving 1 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.118033989 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.118033989 + -1 x = -1.118033989 + -1 Combine like terms: -1.118033989 + -1 = -2.118033989 x = -2.118033989 Simplifying x = -2.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.118033989, -2.118033989}
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