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Simplifying x2 + -59x + -96 = 0 Reorder the terms: -96 + -59x + x2 = 0 Solving -96 + -59x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -59x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -59x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -59x + x2 = 0 + 96 -59x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -59x + x2 = 96 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 = 96 + 870.25 Reorder the terms: 870.25 + -59x + x2 = 96 + 870.25 Combine like terms: 96 + 870.25 = 966.25 870.25 + -59x + x2 = 966.25 Factor a perfect square on the left side: (x + -29.5)(x + -29.5) = 966.25 Calculate the square root of the right side: 31.084562085 Break this problem into two subproblems by setting (x + -29.5) equal to 31.084562085 and -31.084562085.Subproblem 1
x + -29.5 = 31.084562085 Simplifying x + -29.5 = 31.084562085 Reorder the terms: -29.5 + x = 31.084562085 Solving -29.5 + x = 31.084562085 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 = 31.084562085 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = 31.084562085 + 29.5 x = 31.084562085 + 29.5 Combine like terms: 31.084562085 + 29.5 = 60.584562085 x = 60.584562085 Simplifying x = 60.584562085Subproblem 2
x + -29.5 = -31.084562085 Simplifying x + -29.5 = -31.084562085 Reorder the terms: -29.5 + x = -31.084562085 Solving -29.5 + x = -31.084562085 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 = -31.084562085 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = -31.084562085 + 29.5 x = -31.084562085 + 29.5 Combine like terms: -31.084562085 + 29.5 = -1.584562085 x = -1.584562085 Simplifying x = -1.584562085Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.584562085, -1.584562085}
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