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Simplifying 3x2 + -80x + 170 = 0 Reorder the terms: 170 + -80x + 3x2 = 0 Solving 170 + -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'. 56.66666667 + -26.66666667x + x2 = 0 Move the constant term to the right: Add '-56.66666667' to each side of the equation. 56.66666667 + -26.66666667x + -56.66666667 + x2 = 0 + -56.66666667 Reorder the terms: 56.66666667 + -56.66666667 + -26.66666667x + x2 = 0 + -56.66666667 Combine like terms: 56.66666667 + -56.66666667 = 0.00000000 0.00000000 + -26.66666667x + x2 = 0 + -56.66666667 -26.66666667x + x2 = 0 + -56.66666667 Combine like terms: 0 + -56.66666667 = -56.66666667 -26.66666667x + x2 = -56.66666667 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 = -56.66666667 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667x + x2 = -56.66666667 + 177.7777780 Combine like terms: -56.66666667 + 177.7777780 = 121.11111133 177.7777780 + -26.66666667x + x2 = 121.11111133 Factor a perfect square on the left side: (x + -13.33333334)(x + -13.33333334) = 121.11111133 Calculate the square root of the right side: 11.005049356 Break this problem into two subproblems by setting (x + -13.33333334) equal to 11.005049356 and -11.005049356.Subproblem 1
x + -13.33333334 = 11.005049356 Simplifying x + -13.33333334 = 11.005049356 Reorder the terms: -13.33333334 + x = 11.005049356 Solving -13.33333334 + x = 11.005049356 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 = 11.005049356 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = 11.005049356 + 13.33333334 x = 11.005049356 + 13.33333334 Combine like terms: 11.005049356 + 13.33333334 = 24.338382696 x = 24.338382696 Simplifying x = 24.338382696Subproblem 2
x + -13.33333334 = -11.005049356 Simplifying x + -13.33333334 = -11.005049356 Reorder the terms: -13.33333334 + x = -11.005049356 Solving -13.33333334 + x = -11.005049356 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 = -11.005049356 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + x = -11.005049356 + 13.33333334 x = -11.005049356 + 13.33333334 Combine like terms: -11.005049356 + 13.33333334 = 2.328283984 x = 2.328283984 Simplifying x = 2.328283984Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.338382696, 2.328283984}
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