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Simplifying 400 + -80x + -3x2 = 0 Solving 400 + -80x + -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'. -133.3333333 + 26.66666667x + x2 = 0 Move the constant term to the right: Add '133.3333333' to each side of the equation. -133.3333333 + 26.66666667x + 133.3333333 + x2 = 0 + 133.3333333 Reorder the terms: -133.3333333 + 133.3333333 + 26.66666667x + x2 = 0 + 133.3333333 Combine like terms: -133.3333333 + 133.3333333 = 0.0000000 0.0000000 + 26.66666667x + x2 = 0 + 133.3333333 26.66666667x + x2 = 0 + 133.3333333 Combine like terms: 0 + 133.3333333 = 133.3333333 26.66666667x + x2 = 133.3333333 The x term is 26.66666667x. Take half its coefficient (13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. 26.66666667x + 177.7777780 + x2 = 133.3333333 + 177.7777780 Reorder the terms: 177.7777780 + 26.66666667x + x2 = 133.3333333 + 177.7777780 Combine like terms: 133.3333333 + 177.7777780 = 311.1111113 177.7777780 + 26.66666667x + x2 = 311.1111113 Factor a perfect square on the left side: (x + 13.33333334)(x + 13.33333334) = 311.1111113 Calculate the square root of the right side: 17.638342079 Break this problem into two subproblems by setting (x + 13.33333334) equal to 17.638342079 and -17.638342079.Subproblem 1
x + 13.33333334 = 17.638342079 Simplifying x + 13.33333334 = 17.638342079 Reorder the terms: 13.33333334 + x = 17.638342079 Solving 13.33333334 + x = 17.638342079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = 17.638342079 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = 17.638342079 + -13.33333334 x = 17.638342079 + -13.33333334 Combine like terms: 17.638342079 + -13.33333334 = 4.305008739 x = 4.305008739 Simplifying x = 4.305008739Subproblem 2
x + 13.33333334 = -17.638342079 Simplifying x + 13.33333334 = -17.638342079 Reorder the terms: 13.33333334 + x = -17.638342079 Solving 13.33333334 + x = -17.638342079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = -17.638342079 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = -17.638342079 + -13.33333334 x = -17.638342079 + -13.33333334 Combine like terms: -17.638342079 + -13.33333334 = -30.971675419 x = -30.971675419 Simplifying x = -30.971675419Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.305008739, -30.971675419}
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