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Simplifying X2 + -33X + 234 = 0 Reorder the terms: 234 + -33X + X2 = 0 Solving 234 + -33X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-234' to each side of the equation. 234 + -33X + -234 + X2 = 0 + -234 Reorder the terms: 234 + -234 + -33X + X2 = 0 + -234 Combine like terms: 234 + -234 = 0 0 + -33X + X2 = 0 + -234 -33X + X2 = 0 + -234 Combine like terms: 0 + -234 = -234 -33X + X2 = -234 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 = -234 + 272.25 Reorder the terms: 272.25 + -33X + X2 = -234 + 272.25 Combine like terms: -234 + 272.25 = 38.25 272.25 + -33X + X2 = 38.25 Factor a perfect square on the left side: (X + -16.5)(X + -16.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (X + -16.5) equal to 6.184658438 and -6.184658438.Subproblem 1
X + -16.5 = 6.184658438 Simplifying X + -16.5 = 6.184658438 Reorder the terms: -16.5 + X = 6.184658438 Solving -16.5 + X = 6.184658438 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 = 6.184658438 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + X = 6.184658438 + 16.5 X = 6.184658438 + 16.5 Combine like terms: 6.184658438 + 16.5 = 22.684658438 X = 22.684658438 Simplifying X = 22.684658438Subproblem 2
X + -16.5 = -6.184658438 Simplifying X + -16.5 = -6.184658438 Reorder the terms: -16.5 + X = -6.184658438 Solving -16.5 + X = -6.184658438 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 = -6.184658438 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + X = -6.184658438 + 16.5 X = -6.184658438 + 16.5 Combine like terms: -6.184658438 + 16.5 = 10.315341562 X = 10.315341562 Simplifying X = 10.315341562Solution
The solution to the problem is based on the solutions from the subproblems. X = {22.684658438, 10.315341562}
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