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Simplifying x2 + -33x + 240 = 0 Reorder the terms: 240 + -33x + x2 = 0 Solving 240 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-240' to each side of the equation. 240 + -33x + -240 + x2 = 0 + -240 Reorder the terms: 240 + -240 + -33x + x2 = 0 + -240 Combine like terms: 240 + -240 = 0 0 + -33x + x2 = 0 + -240 -33x + x2 = 0 + -240 Combine like terms: 0 + -240 = -240 -33x + x2 = -240 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 = -240 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -240 + 272.25 Combine like terms: -240 + 272.25 = 32.25 272.25 + -33x + x2 = 32.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -16.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -16.5 = 5.678908346 Simplifying x + -16.5 = 5.678908346 Reorder the terms: -16.5 + x = 5.678908346 Solving -16.5 + x = 5.678908346 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 = 5.678908346 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 5.678908346 + 16.5 x = 5.678908346 + 16.5 Combine like terms: 5.678908346 + 16.5 = 22.178908346 x = 22.178908346 Simplifying x = 22.178908346Subproblem 2
x + -16.5 = -5.678908346 Simplifying x + -16.5 = -5.678908346 Reorder the terms: -16.5 + x = -5.678908346 Solving -16.5 + x = -5.678908346 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 = -5.678908346 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -5.678908346 + 16.5 x = -5.678908346 + 16.5 Combine like terms: -5.678908346 + 16.5 = 10.821091654 x = 10.821091654 Simplifying x = 10.821091654Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.178908346, 10.821091654}
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