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Simplifying 3x2 + -68x + 30 = 0 Reorder the terms: 30 + -68x + 3x2 = 0 Solving 30 + -68x + 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'. 10 + -22.66666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -22.66666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -22.66666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -22.66666667x + x2 = 0 + -10 -22.66666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -22.66666667x + x2 = -10 The x term is -22.66666667x. Take half its coefficient (-11.33333334). Square it (128.4444446) and add it to both sides. Add '128.4444446' to each side of the equation. -22.66666667x + 128.4444446 + x2 = -10 + 128.4444446 Reorder the terms: 128.4444446 + -22.66666667x + x2 = -10 + 128.4444446 Combine like terms: -10 + 128.4444446 = 118.4444446 128.4444446 + -22.66666667x + x2 = 118.4444446 Factor a perfect square on the left side: (x + -11.33333334)(x + -11.33333334) = 118.4444446 Calculate the square root of the right side: 10.883218485 Break this problem into two subproblems by setting (x + -11.33333334) equal to 10.883218485 and -10.883218485.Subproblem 1
x + -11.33333334 = 10.883218485 Simplifying x + -11.33333334 = 10.883218485 Reorder the terms: -11.33333334 + x = 10.883218485 Solving -11.33333334 + x = 10.883218485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = 10.883218485 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = 10.883218485 + 11.33333334 x = 10.883218485 + 11.33333334 Combine like terms: 10.883218485 + 11.33333334 = 22.216551825 x = 22.216551825 Simplifying x = 22.216551825Subproblem 2
x + -11.33333334 = -10.883218485 Simplifying x + -11.33333334 = -10.883218485 Reorder the terms: -11.33333334 + x = -10.883218485 Solving -11.33333334 + x = -10.883218485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = -10.883218485 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = -10.883218485 + 11.33333334 x = -10.883218485 + 11.33333334 Combine like terms: -10.883218485 + 11.33333334 = 0.450114855 x = 0.450114855 Simplifying x = 0.450114855Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.216551825, 0.450114855}
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