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Simplifying x2 + 41x + 132 = 0 Reorder the terms: 132 + 41x + x2 = 0 Solving 132 + 41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-132' to each side of the equation. 132 + 41x + -132 + x2 = 0 + -132 Reorder the terms: 132 + -132 + 41x + x2 = 0 + -132 Combine like terms: 132 + -132 = 0 0 + 41x + x2 = 0 + -132 41x + x2 = 0 + -132 Combine like terms: 0 + -132 = -132 41x + x2 = -132 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = -132 + 420.25 Reorder the terms: 420.25 + 41x + x2 = -132 + 420.25 Combine like terms: -132 + 420.25 = 288.25 420.25 + 41x + x2 = 288.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (x + 20.5) equal to 16.977926846 and -16.977926846.Subproblem 1
x + 20.5 = 16.977926846 Simplifying x + 20.5 = 16.977926846 Reorder the terms: 20.5 + x = 16.977926846 Solving 20.5 + x = 16.977926846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 16.977926846 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 16.977926846 + -20.5 x = 16.977926846 + -20.5 Combine like terms: 16.977926846 + -20.5 = -3.522073154 x = -3.522073154 Simplifying x = -3.522073154Subproblem 2
x + 20.5 = -16.977926846 Simplifying x + 20.5 = -16.977926846 Reorder the terms: 20.5 + x = -16.977926846 Solving 20.5 + x = -16.977926846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -16.977926846 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -16.977926846 + -20.5 x = -16.977926846 + -20.5 Combine like terms: -16.977926846 + -20.5 = -37.477926846 x = -37.477926846 Simplifying x = -37.477926846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.522073154, -37.477926846}
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