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Simplifying 3x2 + -80x + 100 = 0 Reorder the terms: 100 + -80x + 3x2 = 0 Solving 100 + -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'. 33.33333333 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + -26.66666667x + -33.33333333 + x2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + -26.66666667x + x2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + -26.66666667x + x2 = 0 + -33.33333333 -26.66666667x + x2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 -26.66666667x + x2 = -33.33333333 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 = -33.33333333 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -33.33333333 + 177.7777780 Combine like terms: -33.33333333 + 177.7777780 = 144.44444467 177.7777780 + -26.66666667x + x2 = 144.44444467 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 144.44444467 Calculate the square root of the right side: 12.018504261 Break this problem into two subproblems by setting (x + -13.33333334) equal to 12.018504261 and -12.018504261.Subproblem 1
x + -13.33333334 = 12.018504261 Simplifying x + -13.33333334 = 12.018504261 Reorder the terms: -13.33333334 + x = 12.018504261 Solving -13.33333334 + x = 12.018504261 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 = 12.018504261 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 12.018504261 + 13.33333334 x = 12.018504261 + 13.33333334 Combine like terms: 12.018504261 + 13.33333334 = 25.351837601 x = 25.351837601 Simplifying x = 25.351837601Subproblem 2
x + -13.33333334 = -12.018504261 Simplifying x + -13.33333334 = -12.018504261 Reorder the terms: -13.33333334 + x = -12.018504261 Solving -13.33333334 + x = -12.018504261 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 = -12.018504261 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -12.018504261 + 13.33333334 x = -12.018504261 + 13.33333334 Combine like terms: -12.018504261 + 13.33333334 = 1.314829079 x = 1.314829079 Simplifying x = 1.314829079Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.351837601, 1.314829079}
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