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Simplifying x2 + x + -1.134 = 0 Reorder the terms: -1.134 + x + x2 = 0 Solving -1.134 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.134' to each side of the equation. -1.134 + x + 1.134 + x2 = 0 + 1.134 Reorder the terms: -1.134 + 1.134 + x + x2 = 0 + 1.134 Combine like terms: -1.134 + 1.134 = 0.000 0.000 + x + x2 = 0 + 1.134 x + x2 = 0 + 1.134 Combine like terms: 0 + 1.134 = 1.134 x + x2 = 1.134 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. x + 0.25 + x2 = 1.134 + 0.25 Reorder the terms: 0.25 + x + x2 = 1.134 + 0.25 Combine like terms: 1.134 + 0.25 = 1.384 0.25 + x + x2 = 1.384 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.384 Calculate the square root of the right side: 1.176435294 Break this problem into two subproblems by setting (x + 0.5) equal to 1.176435294 and -1.176435294.Subproblem 1
x + 0.5 = 1.176435294 Simplifying x + 0.5 = 1.176435294 Reorder the terms: 0.5 + x = 1.176435294 Solving 0.5 + x = 1.176435294 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 = 1.176435294 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.176435294 + -0.5 x = 1.176435294 + -0.5 Combine like terms: 1.176435294 + -0.5 = 0.676435294 x = 0.676435294 Simplifying x = 0.676435294Subproblem 2
x + 0.5 = -1.176435294 Simplifying x + 0.5 = -1.176435294 Reorder the terms: 0.5 + x = -1.176435294 Solving 0.5 + x = -1.176435294 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 = -1.176435294 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.176435294 + -0.5 x = -1.176435294 + -0.5 Combine like terms: -1.176435294 + -0.5 = -1.676435294 x = -1.676435294 Simplifying x = -1.676435294Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.676435294, -1.676435294}
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