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Simplifying 3x2 + -80x + 80 = 0 Reorder the terms: 80 + -80x + 3x2 = 0 Solving 80 + -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'. 26.66666667 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-26.66666667' to each side of the equation. 26.66666667 + -26.66666667x + -26.66666667 + x2 = 0 + -26.66666667 Reorder the terms: 26.66666667 + -26.66666667 + -26.66666667x + x2 = 0 + -26.66666667 Combine like terms: 26.66666667 + -26.66666667 = 0.00000000 0.00000000 + -26.66666667x + x2 = 0 + -26.66666667 -26.66666667x + x2 = 0 + -26.66666667 Combine like terms: 0 + -26.66666667 = -26.66666667 -26.66666667x + x2 = -26.66666667 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 = -26.66666667 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -26.66666667 + 177.7777780 Combine like terms: -26.66666667 + 177.7777780 = 151.11111133 177.7777780 + -26.66666667x + x2 = 151.11111133 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 151.11111133 Calculate the square root of the right side: 12.292725952 Break this problem into two subproblems by setting (x + -13.33333334) equal to 12.292725952 and -12.292725952.Subproblem 1
x + -13.33333334 = 12.292725952 Simplifying x + -13.33333334 = 12.292725952 Reorder the terms: -13.33333334 + x = 12.292725952 Solving -13.33333334 + x = 12.292725952 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 = 12.292725952 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 12.292725952 + 13.33333334 x = 12.292725952 + 13.33333334 Combine like terms: 12.292725952 + 13.33333334 = 25.626059292 x = 25.626059292 Simplifying x = 25.626059292Subproblem 2
x + -13.33333334 = -12.292725952 Simplifying x + -13.33333334 = -12.292725952 Reorder the terms: -13.33333334 + x = -12.292725952 Solving -13.33333334 + x = -12.292725952 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 = -12.292725952 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -12.292725952 + 13.33333334 x = -12.292725952 + 13.33333334 Combine like terms: -12.292725952 + 13.33333334 = 1.040607388 x = 1.040607388 Simplifying x = 1.040607388Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.626059292, 1.040607388}
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