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Simplifying ((0.0001185X2) + -1(0.009X) + (0.0613)) = 0 Remove parenthesis around (0.009X) ((0.0001185X2) + -1 * 0.009X + (0.0613)) = 0 Multiply -1 * 0.009 ((0.0001185X2) + -0.009X + (0.0613)) = 0 ((0.0001185X2) + -0.009X + 0.0613) = 0 Reorder the terms: (0.0613 + -0.009X + (0.0001185X2)) = 0 Remove parenthesis around (0.0613 + -0.009X + (0.0001185X2)) 0.0613 + -0.009X + (0.0001185X2) = 0 Solving 0.0613 + -0.009X + (0.0001185X2) = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.0001185 the coefficient of the squared term: Divide each side by '0.0001185'. 517.2995781 + -75.94936709X + X2 = 0 Move the constant term to the right: Add '-517.2995781' to each side of the equation. 517.2995781 + -75.94936709X + -517.2995781 + X2 = 0 + -517.2995781 Reorder the terms: 517.2995781 + -517.2995781 + -75.94936709X + X2 = 0 + -517.2995781 Combine like terms: 517.2995781 + -517.2995781 = 0.0000000 0.0000000 + -75.94936709X + X2 = 0 + -517.2995781 -75.94936709X + X2 = 0 + -517.2995781 Combine like terms: 0 + -517.2995781 = -517.2995781 -75.94936709X + X2 = -517.2995781 The X term is -75.94936709X. Take half its coefficient (-37.97468355). Square it (1442.076591) and add it to both sides. Add '1442.076591' to each side of the equation. -75.94936709X + 1442.076591 + X2 = -517.2995781 + 1442.076591 Reorder the terms: 1442.076591 + -75.94936709X + X2 = -517.2995781 + 1442.076591 Combine like terms: -517.2995781 + 1442.076591 = 924.7770129 1442.076591 + -75.94936709X + X2 = 924.7770129 Factor a perfect square on the left side: ((X) + -37.97468355)((X) + -37.97468355) = 924.7770129 Calculate the square root of the right side: 30.410146545 Break this problem into two subproblems by setting ((X) + -37.97468355) equal to 30.410146545 and -30.410146545.Subproblem 1
(X) + -37.97468355 = 30.410146545 Simplifying (X) + -37.97468355 = 30.410146545 X + -37.97468355 = 30.410146545 Reorder the terms: -37.97468355 + X = 30.410146545 Solving -37.97468355 + X = 30.410146545 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '37.97468355' to each side of the equation. -37.97468355 + 37.97468355 + X = 30.410146545 + 37.97468355 Combine like terms: -37.97468355 + 37.97468355 = 0.00000000 0.00000000 + X = 30.410146545 + 37.97468355 X = 30.410146545 + 37.97468355 Combine like terms: 30.410146545 + 37.97468355 = 68.384830095 X = 68.384830095 Simplifying X = 68.384830095Subproblem 2
(X) + -37.97468355 = -30.410146545 Simplifying (X) + -37.97468355 = -30.410146545 X + -37.97468355 = -30.410146545 Reorder the terms: -37.97468355 + X = -30.410146545 Solving -37.97468355 + X = -30.410146545 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '37.97468355' to each side of the equation. -37.97468355 + 37.97468355 + X = -30.410146545 + 37.97468355 Combine like terms: -37.97468355 + 37.97468355 = 0.00000000 0.00000000 + X = -30.410146545 + 37.97468355 X = -30.410146545 + 37.97468355 Combine like terms: -30.410146545 + 37.97468355 = 7.564537005 X = 7.564537005 Simplifying X = 7.564537005Solution
The solution to the problem is based on the solutions from the subproblems. X = {68.384830095, 7.564537005}
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