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Simplifying x2 + 1.73x + -1 = 0 Reorder the terms: -1 + 1.73x + x2 = 0 Solving -1 + 1.73x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.73x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.73x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.73x + x2 = 0 + 1 1.73x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.73x + x2 = 1 The x term is 1.73x. Take half its coefficient (0.865). Square it (0.748225) and add it to both sides. Add '0.748225' to each side of the equation. 1.73x + 0.748225 + x2 = 1 + 0.748225 Reorder the terms: 0.748225 + 1.73x + x2 = 1 + 0.748225 Combine like terms: 1 + 0.748225 = 1.748225 0.748225 + 1.73x + x2 = 1.748225 Factor a perfect square on the left side: (x + 0.865)(x + 0.865) = 1.748225 Calculate the square root of the right side: 1.322204598 Break this problem into two subproblems by setting (x + 0.865) equal to 1.322204598 and -1.322204598.Subproblem 1
x + 0.865 = 1.322204598 Simplifying x + 0.865 = 1.322204598 Reorder the terms: 0.865 + x = 1.322204598 Solving 0.865 + x = 1.322204598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.865' to each side of the equation. 0.865 + -0.865 + x = 1.322204598 + -0.865 Combine like terms: 0.865 + -0.865 = 0.000 0.000 + x = 1.322204598 + -0.865 x = 1.322204598 + -0.865 Combine like terms: 1.322204598 + -0.865 = 0.457204598 x = 0.457204598 Simplifying x = 0.457204598Subproblem 2
x + 0.865 = -1.322204598 Simplifying x + 0.865 = -1.322204598 Reorder the terms: 0.865 + x = -1.322204598 Solving 0.865 + x = -1.322204598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.865' to each side of the equation. 0.865 + -0.865 + x = -1.322204598 + -0.865 Combine like terms: 0.865 + -0.865 = 0.000 0.000 + x = -1.322204598 + -0.865 x = -1.322204598 + -0.865 Combine like terms: -1.322204598 + -0.865 = -2.187204598 x = -2.187204598 Simplifying x = -2.187204598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.457204598, -2.187204598}
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