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Simplifying 3x2 + -80x + 800 = 600 Reorder the terms: 800 + -80x + 3x2 = 600 Solving 800 + -80x + 3x2 = 600 Solving for variable 'x'. Reorder the terms: 800 + -600 + -80x + 3x2 = 600 + -600 Combine like terms: 800 + -600 = 200 200 + -80x + 3x2 = 600 + -600 Combine like terms: 600 + -600 = 0 200 + -80x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 66.66666667 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-66.66666667' to each side of the equation. 66.66666667 + -26.66666667x + -66.66666667 + x2 = 0 + -66.66666667 Reorder the terms: 66.66666667 + -66.66666667 + -26.66666667x + x2 = 0 + -66.66666667 Combine like terms: 66.66666667 + -66.66666667 = 0.00000000 0.00000000 + -26.66666667x + x2 = 0 + -66.66666667 -26.66666667x + x2 = 0 + -66.66666667 Combine like terms: 0 + -66.66666667 = -66.66666667 -26.66666667x + x2 = -66.66666667 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 = -66.66666667 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -66.66666667 + 177.7777780 Combine like terms: -66.66666667 + 177.7777780 = 111.11111133 177.7777780 + -26.66666667x + x2 = 111.11111133 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 111.11111133 Calculate the square root of the right side: 10.540925544 Break this problem into two subproblems by setting (x + -13.33333334) equal to 10.540925544 and -10.540925544.Subproblem 1
x + -13.33333334 = 10.540925544 Simplifying x + -13.33333334 = 10.540925544 Reorder the terms: -13.33333334 + x = 10.540925544 Solving -13.33333334 + x = 10.540925544 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 = 10.540925544 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 10.540925544 + 13.33333334 x = 10.540925544 + 13.33333334 Combine like terms: 10.540925544 + 13.33333334 = 23.874258884 x = 23.874258884 Simplifying x = 23.874258884Subproblem 2
x + -13.33333334 = -10.540925544 Simplifying x + -13.33333334 = -10.540925544 Reorder the terms: -13.33333334 + x = -10.540925544 Solving -13.33333334 + x = -10.540925544 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 = -10.540925544 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -10.540925544 + 13.33333334 x = -10.540925544 + 13.33333334 Combine like terms: -10.540925544 + 13.33333334 = 2.792407796 x = 2.792407796 Simplifying x = 2.792407796Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.874258884, 2.792407796}
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