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Simplifying 55 = 3X(20 + -1X) 55 = (20 * 3X + -1X * 3X) 55 = (60X + -3X2) Solving 55 = 60X + -3X2 Solving for variable 'X'. Reorder the terms: 55 + -60X + 3X2 = 60X + -60X + -3X2 + 3X2 Combine like terms: 60X + -60X = 0 55 + -60X + 3X2 = 0 + -3X2 + 3X2 55 + -60X + 3X2 = -3X2 + 3X2 Combine like terms: -3X2 + 3X2 = 0 55 + -60X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 18.33333333 + -20X + X2 = 0 Move the constant term to the right: Add '-18.33333333' to each side of the equation. 18.33333333 + -20X + -18.33333333 + X2 = 0 + -18.33333333 Reorder the terms: 18.33333333 + -18.33333333 + -20X + X2 = 0 + -18.33333333 Combine like terms: 18.33333333 + -18.33333333 = 0.00000000 0.00000000 + -20X + X2 = 0 + -18.33333333 -20X + X2 = 0 + -18.33333333 Combine like terms: 0 + -18.33333333 = -18.33333333 -20X + X2 = -18.33333333 The X term is -20X. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20X + 100 + X2 = -18.33333333 + 100 Reorder the terms: 100 + -20X + X2 = -18.33333333 + 100 Combine like terms: -18.33333333 + 100 = 81.66666667 100 + -20X + X2 = 81.66666667 Factor a perfect square on the left side: (X + -10)(X + -10) = 81.66666667 Calculate the square root of the right side: 9.036961141 Break this problem into two subproblems by setting (X + -10) equal to 9.036961141 and -9.036961141.Subproblem 1
X + -10 = 9.036961141 Simplifying X + -10 = 9.036961141 Reorder the terms: -10 + X = 9.036961141 Solving -10 + X = 9.036961141 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + X = 9.036961141 + 10 Combine like terms: -10 + 10 = 0 0 + X = 9.036961141 + 10 X = 9.036961141 + 10 Combine like terms: 9.036961141 + 10 = 19.036961141 X = 19.036961141 Simplifying X = 19.036961141Subproblem 2
X + -10 = -9.036961141 Simplifying X + -10 = -9.036961141 Reorder the terms: -10 + X = -9.036961141 Solving -10 + X = -9.036961141 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + X = -9.036961141 + 10 Combine like terms: -10 + 10 = 0 0 + X = -9.036961141 + 10 X = -9.036961141 + 10 Combine like terms: -9.036961141 + 10 = 0.963038859 X = 0.963038859 Simplifying X = 0.963038859Solution
The solution to the problem is based on the solutions from the subproblems. X = {19.036961141, 0.963038859}
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