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Simplifying x2 + 71x + 72 = 0 Reorder the terms: 72 + 71x + x2 = 0 Solving 72 + 71x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + 71x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + 71x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + 71x + x2 = 0 + -72 71x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 71x + x2 = -72 The x term is 71x. Take half its coefficient (35.5). Square it (1260.25) and add it to both sides. Add '1260.25' to each side of the equation. 71x + 1260.25 + x2 = -72 + 1260.25 Reorder the terms: 1260.25 + 71x + x2 = -72 + 1260.25 Combine like terms: -72 + 1260.25 = 1188.25 1260.25 + 71x + x2 = 1188.25 Factor a perfect square on the left side: (x + 35.5)(x + 35.5) = 1188.25 Calculate the square root of the right side: 34.471002306 Break this problem into two subproblems by setting (x + 35.5) equal to 34.471002306 and -34.471002306.Subproblem 1
x + 35.5 = 34.471002306 Simplifying x + 35.5 = 34.471002306 Reorder the terms: 35.5 + x = 34.471002306 Solving 35.5 + x = 34.471002306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x = 34.471002306 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = 34.471002306 + -35.5 x = 34.471002306 + -35.5 Combine like terms: 34.471002306 + -35.5 = -1.028997694 x = -1.028997694 Simplifying x = -1.028997694Subproblem 2
x + 35.5 = -34.471002306 Simplifying x + 35.5 = -34.471002306 Reorder the terms: 35.5 + x = -34.471002306 Solving 35.5 + x = -34.471002306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x = -34.471002306 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = -34.471002306 + -35.5 x = -34.471002306 + -35.5 Combine like terms: -34.471002306 + -35.5 = -69.971002306 x = -69.971002306 Simplifying x = -69.971002306Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.028997694, -69.971002306}
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