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Simplifying x2 + 71x + -180 = 0 Reorder the terms: -180 + 71x + x2 = 0 Solving -180 + 71x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 71x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 71x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 71x + x2 = 0 + 180 71x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 71x + x2 = 180 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 = 180 + 1260.25 Reorder the terms: 1260.25 + 71x + x2 = 180 + 1260.25 Combine like terms: 180 + 1260.25 = 1440.25 1260.25 + 71x + x2 = 1440.25 Factor a perfect square on the left side: (x + 35.5)(x + 35.5) = 1440.25 Calculate the square root of the right side: 37.950625818 Break this problem into two subproblems by setting (x + 35.5) equal to 37.950625818 and -37.950625818.Subproblem 1
x + 35.5 = 37.950625818 Simplifying x + 35.5 = 37.950625818 Reorder the terms: 35.5 + x = 37.950625818 Solving 35.5 + x = 37.950625818 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 = 37.950625818 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = 37.950625818 + -35.5 x = 37.950625818 + -35.5 Combine like terms: 37.950625818 + -35.5 = 2.450625818 x = 2.450625818 Simplifying x = 2.450625818Subproblem 2
x + 35.5 = -37.950625818 Simplifying x + 35.5 = -37.950625818 Reorder the terms: 35.5 + x = -37.950625818 Solving 35.5 + x = -37.950625818 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 = -37.950625818 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = -37.950625818 + -35.5 x = -37.950625818 + -35.5 Combine like terms: -37.950625818 + -35.5 = -73.450625818 x = -73.450625818 Simplifying x = -73.450625818Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.450625818, -73.450625818}
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