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Simplifying x2 + 59x + 60 = 0 Reorder the terms: 60 + 59x + x2 = 0 Solving 60 + 59x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 59x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 59x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 59x + x2 = 0 + -60 59x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 59x + x2 = -60 The x term is 59x. Take half its coefficient (29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. 59x + 870.25 + x2 = -60 + 870.25 Reorder the terms: 870.25 + 59x + x2 = -60 + 870.25 Combine like terms: -60 + 870.25 = 810.25 870.25 + 59x + x2 = 810.25 Factor a perfect square on the left side: (x + 29.5)(x + 29.5) = 810.25 Calculate the square root of the right side: 28.464890655 Break this problem into two subproblems by setting (x + 29.5) equal to 28.464890655 and -28.464890655.Subproblem 1
x + 29.5 = 28.464890655 Simplifying x + 29.5 = 28.464890655 Reorder the terms: 29.5 + x = 28.464890655 Solving 29.5 + x = 28.464890655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = 28.464890655 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = 28.464890655 + -29.5 x = 28.464890655 + -29.5 Combine like terms: 28.464890655 + -29.5 = -1.035109345 x = -1.035109345 Simplifying x = -1.035109345Subproblem 2
x + 29.5 = -28.464890655 Simplifying x + 29.5 = -28.464890655 Reorder the terms: 29.5 + x = -28.464890655 Solving 29.5 + x = -28.464890655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = -28.464890655 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = -28.464890655 + -29.5 x = -28.464890655 + -29.5 Combine like terms: -28.464890655 + -29.5 = -57.964890655 x = -57.964890655 Simplifying x = -57.964890655Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.035109345, -57.964890655}
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