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Simplifying x2 + -0.66x + -1.32 = 0 Reorder the terms: -1.32 + -0.66x + x2 = 0 Solving -1.32 + -0.66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.32' to each side of the equation. -1.32 + -0.66x + 1.32 + x2 = 0 + 1.32 Reorder the terms: -1.32 + 1.32 + -0.66x + x2 = 0 + 1.32 Combine like terms: -1.32 + 1.32 = 0.00 0.00 + -0.66x + x2 = 0 + 1.32 -0.66x + x2 = 0 + 1.32 Combine like terms: 0 + 1.32 = 1.32 -0.66x + x2 = 1.32 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 = 1.32 + 0.1089 Reorder the terms: 0.1089 + -0.66x + x2 = 1.32 + 0.1089 Combine like terms: 1.32 + 0.1089 = 1.4289 0.1089 + -0.66x + x2 = 1.4289 Factor a perfect square on the left side: (x + -0.33)(x + -0.33) = 1.4289 Calculate the square root of the right side: 1.195366053 Break this problem into two subproblems by setting (x + -0.33) equal to 1.195366053 and -1.195366053.Subproblem 1
x + -0.33 = 1.195366053 Simplifying x + -0.33 = 1.195366053 Reorder the terms: -0.33 + x = 1.195366053 Solving -0.33 + x = 1.195366053 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 = 1.195366053 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + x = 1.195366053 + 0.33 x = 1.195366053 + 0.33 Combine like terms: 1.195366053 + 0.33 = 1.525366053 x = 1.525366053 Simplifying x = 1.525366053Subproblem 2
x + -0.33 = -1.195366053 Simplifying x + -0.33 = -1.195366053 Reorder the terms: -0.33 + x = -1.195366053 Solving -0.33 + x = -1.195366053 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 = -1.195366053 + 0.33 Combine like terms: -0.33 + 0.33 = 0.00 0.00 + x = -1.195366053 + 0.33 x = -1.195366053 + 0.33 Combine like terms: -1.195366053 + 0.33 = -0.865366053 x = -0.865366053 Simplifying x = -0.865366053Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.525366053, -0.865366053}
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