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Simplifying x2 + 33x + 59 = 0 Reorder the terms: 59 + 33x + x2 = 0 Solving 59 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 33x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 33x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 33x + x2 = 0 + -59 33x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 33x + x2 = -59 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = -59 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -59 + 272.25 Combine like terms: -59 + 272.25 = 213.25 272.25 + 33x + x2 = 213.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 213.25 Calculate the square root of the right side: 14.603081867 Break this problem into two subproblems by setting (x + 16.5) equal to 14.603081867 and -14.603081867.Subproblem 1
x + 16.5 = 14.603081867 Simplifying x + 16.5 = 14.603081867 Reorder the terms: 16.5 + x = 14.603081867 Solving 16.5 + x = 14.603081867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 14.603081867 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 14.603081867 + -16.5 x = 14.603081867 + -16.5 Combine like terms: 14.603081867 + -16.5 = -1.896918133 x = -1.896918133 Simplifying x = -1.896918133Subproblem 2
x + 16.5 = -14.603081867 Simplifying x + 16.5 = -14.603081867 Reorder the terms: 16.5 + x = -14.603081867 Solving 16.5 + x = -14.603081867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -14.603081867 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -14.603081867 + -16.5 x = -14.603081867 + -16.5 Combine like terms: -14.603081867 + -16.5 = -31.103081867 x = -31.103081867 Simplifying x = -31.103081867Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.896918133, -31.103081867}
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