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Simplifying 9600 + -400X + 3X2 = 0 Solving 9600 + -400X + 3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3200 + -133.3333333X + X2 = 0 Move the constant term to the right: Add '-3200' to each side of the equation. 3200 + -133.3333333X + -3200 + X2 = 0 + -3200 Reorder the terms: 3200 + -3200 + -133.3333333X + X2 = 0 + -3200 Combine like terms: 3200 + -3200 = 0 0 + -133.3333333X + X2 = 0 + -3200 -133.3333333X + X2 = 0 + -3200 Combine like terms: 0 + -3200 = -3200 -133.3333333X + X2 = -3200 The X term is -133.3333333X. Take half its coefficient (-66.66666665). Square it (4444.444442) and add it to both sides. Add '4444.444442' to each side of the equation. -133.3333333X + 4444.444442 + X2 = -3200 + 4444.444442 Reorder the terms: 4444.444442 + -133.3333333X + X2 = -3200 + 4444.444442 Combine like terms: -3200 + 4444.444442 = 1244.444442 4444.444442 + -133.3333333X + X2 = 1244.444442 Factor a perfect square on the left side: (X + -66.66666665)(X + -66.66666665) = 1244.444442 Calculate the square root of the right side: 35.276684113 Break this problem into two subproblems by setting (X + -66.66666665) equal to 35.276684113 and -35.276684113.Subproblem 1
X + -66.66666665 = 35.276684113 Simplifying X + -66.66666665 = 35.276684113 Reorder the terms: -66.66666665 + X = 35.276684113 Solving -66.66666665 + X = 35.276684113 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + X = 35.276684113 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + X = 35.276684113 + 66.66666665 X = 35.276684113 + 66.66666665 Combine like terms: 35.276684113 + 66.66666665 = 101.943350763 X = 101.943350763 Simplifying X = 101.943350763Subproblem 2
X + -66.66666665 = -35.276684113 Simplifying X + -66.66666665 = -35.276684113 Reorder the terms: -66.66666665 + X = -35.276684113 Solving -66.66666665 + X = -35.276684113 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + X = -35.276684113 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + X = -35.276684113 + 66.66666665 X = -35.276684113 + 66.66666665 Combine like terms: -35.276684113 + 66.66666665 = 31.389982537 X = 31.389982537 Simplifying X = 31.389982537Solution
The solution to the problem is based on the solutions from the subproblems. X = {101.943350763, 31.389982537}
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