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Simplifying x2 + -33x + 80 = 0 Reorder the terms: 80 + -33x + x2 = 0 Solving 80 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -33x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -33x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -33x + x2 = 0 + -80 -33x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -33x + x2 = -80 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 = -80 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -80 + 272.25 Combine like terms: -80 + 272.25 = 192.25 272.25 + -33x + x2 = 192.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (x + -16.5) equal to 13.865424624 and -13.865424624.Subproblem 1
x + -16.5 = 13.865424624 Simplifying x + -16.5 = 13.865424624 Reorder the terms: -16.5 + x = 13.865424624 Solving -16.5 + x = 13.865424624 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 = 13.865424624 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 13.865424624 + 16.5 x = 13.865424624 + 16.5 Combine like terms: 13.865424624 + 16.5 = 30.365424624 x = 30.365424624 Simplifying x = 30.365424624Subproblem 2
x + -16.5 = -13.865424624 Simplifying x + -16.5 = -13.865424624 Reorder the terms: -16.5 + x = -13.865424624 Solving -16.5 + x = -13.865424624 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 = -13.865424624 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -13.865424624 + 16.5 x = -13.865424624 + 16.5 Combine like terms: -13.865424624 + 16.5 = 2.634575376 x = 2.634575376 Simplifying x = 2.634575376Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.365424624, 2.634575376}
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