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Simplifying x2 + -0.66x + -2.9 = 0 Reorder the terms: -2.9 + -0.66x + x2 = 0 Solving -2.9 + -0.66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.9' to each side of the equation. -2.9 + -0.66x + 2.9 + x2 = 0 + 2.9 Reorder the terms: -2.9 + 2.9 + -0.66x + x2 = 0 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + -0.66x + x2 = 0 + 2.9 -0.66x + x2 = 0 + 2.9 Combine like terms: 0 + 2.9 = 2.9 -0.66x + x2 = 2.9 The x term is -0.66x. Take half its coefficient (-0.33). Square it (0.1089) and add it to both sides. Add '0.1089' to each side of the equation. -0.66x + 0.1089 + x2 = 2.9 + 0.1089 Reorder the terms: 0.1089 + -0.66x + x2 = 2.9 + 0.1089 Combine like terms: 2.9 + 0.1089 = 3.0089 0.1089 + -0.66x + x2 = 3.0089 Factor a perfect square on the left side: (x + -0.33)(x + -0.33) = 3.0089 Calculate the square root of the right side: 1.734618114 Break this problem into two subproblems by setting (x + -0.33) equal to 1.734618114 and -1.734618114.Subproblem 1
x + -0.33 = 1.734618114 Simplifying x + -0.33 = 1.734618114 Reorder the terms: -0.33 + x = 1.734618114 Solving -0.33 + x = 1.734618114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33' to each side of the equation. -0.33 + 0.33 + x = 1.734618114 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + x = 1.734618114 + 0.33 x = 1.734618114 + 0.33 Combine like terms: 1.734618114 + 0.33 = 2.064618114 x = 2.064618114 Simplifying x = 2.064618114Subproblem 2
x + -0.33 = -1.734618114 Simplifying x + -0.33 = -1.734618114 Reorder the terms: -0.33 + x = -1.734618114 Solving -0.33 + x = -1.734618114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.33' to each side of the equation. -0.33 + 0.33 + x = -1.734618114 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + x = -1.734618114 + 0.33 x = -1.734618114 + 0.33 Combine like terms: -1.734618114 + 0.33 = -1.404618114 x = -1.404618114 Simplifying x = -1.404618114Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.064618114, -1.404618114}
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