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Simplifying x2 + 0.58x + -0.4 = 0 Reorder the terms: -0.4 + 0.58x + x2 = 0 Solving -0.4 + 0.58x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.58x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.58x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.58x + x2 = 0 + 0.4 0.58x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.58x + x2 = 0.4 The x term is 0.58x. Take half its coefficient (0.29). Square it (0.0841) and add it to both sides. Add '0.0841' to each side of the equation. 0.58x + 0.0841 + x2 = 0.4 + 0.0841 Reorder the terms: 0.0841 + 0.58x + x2 = 0.4 + 0.0841 Combine like terms: 0.4 + 0.0841 = 0.4841 0.0841 + 0.58x + x2 = 0.4841 Factor a perfect square on the left side: (x + 0.29)(x + 0.29) = 0.4841 Calculate the square root of the right side: 0.695772951 Break this problem into two subproblems by setting (x + 0.29) equal to 0.695772951 and -0.695772951.Subproblem 1
x + 0.29 = 0.695772951 Simplifying x + 0.29 = 0.695772951 Reorder the terms: 0.29 + x = 0.695772951 Solving 0.29 + x = 0.695772951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.29' to each side of the equation. 0.29 + -0.29 + x = 0.695772951 + -0.29 Combine like terms: 0.29 + -0.29 = 0.00 0.00 + x = 0.695772951 + -0.29 x = 0.695772951 + -0.29 Combine like terms: 0.695772951 + -0.29 = 0.405772951 x = 0.405772951 Simplifying x = 0.405772951Subproblem 2
x + 0.29 = -0.695772951 Simplifying x + 0.29 = -0.695772951 Reorder the terms: 0.29 + x = -0.695772951 Solving 0.29 + x = -0.695772951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.29' to each side of the equation. 0.29 + -0.29 + x = -0.695772951 + -0.29 Combine like terms: 0.29 + -0.29 = 0.00 0.00 + x = -0.695772951 + -0.29 x = -0.695772951 + -0.29 Combine like terms: -0.695772951 + -0.29 = -0.985772951 x = -0.985772951 Simplifying x = -0.985772951Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.405772951, -0.985772951}
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