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Simplifying 3x2 + -80x + -2700 = 0 Reorder the terms: -2700 + -80x + 3x2 = 0 Solving -2700 + -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'. -900 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + -26.66666667x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + -26.66666667x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + -26.66666667x + x2 = 0 + 900 -26.66666667x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 -26.66666667x + x2 = 900 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 = 900 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = 900 + 177.7777780 Combine like terms: 900 + 177.7777780 = 1077.777778 177.7777780 + -26.66666667x + x2 = 1077.777778 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 1077.777778 Calculate the square root of the right side: 32.829526009 Break this problem into two subproblems by setting (x + -13.33333334) equal to 32.829526009 and -32.829526009.Subproblem 1
x + -13.33333334 = 32.829526009 Simplifying x + -13.33333334 = 32.829526009 Reorder the terms: -13.33333334 + x = 32.829526009 Solving -13.33333334 + x = 32.829526009 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 = 32.829526009 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 32.829526009 + 13.33333334 x = 32.829526009 + 13.33333334 Combine like terms: 32.829526009 + 13.33333334 = 46.162859349 x = 46.162859349 Simplifying x = 46.162859349Subproblem 2
x + -13.33333334 = -32.829526009 Simplifying x + -13.33333334 = -32.829526009 Reorder the terms: -13.33333334 + x = -32.829526009 Solving -13.33333334 + x = -32.829526009 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 = -32.829526009 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -32.829526009 + 13.33333334 x = -32.829526009 + 13.33333334 Combine like terms: -32.829526009 + 13.33333334 = -19.496192669 x = -19.496192669 Simplifying x = -19.496192669Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.162859349, -19.496192669}
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