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Simplifying 3x2 + -40x + 60 = 0 Reorder the terms: 60 + -40x + 3x2 = 0 Solving 60 + -40x + 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'. 20 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -13.33333333x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -13.33333333x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -13.33333333x + x2 = 0 + -20 -13.33333333x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -13.33333333x + x2 = -20 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = -20 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = -20 + 44.44444442 Combine like terms: -20 + 44.44444442 = 24.44444442 44.44444442 + -13.33333333x + x2 = 24.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 24.44444442 Calculate the square root of the right side: 4.944132322 Break this problem into two subproblems by setting (x + -6.666666665) equal to 4.944132322 and -4.944132322.Subproblem 1
x + -6.666666665 = 4.944132322 Simplifying x + -6.666666665 = 4.944132322 Reorder the terms: -6.666666665 + x = 4.944132322 Solving -6.666666665 + x = 4.944132322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 4.944132322 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 4.944132322 + 6.666666665 x = 4.944132322 + 6.666666665 Combine like terms: 4.944132322 + 6.666666665 = 11.610798987 x = 11.610798987 Simplifying x = 11.610798987Subproblem 2
x + -6.666666665 = -4.944132322 Simplifying x + -6.666666665 = -4.944132322 Reorder the terms: -6.666666665 + x = -4.944132322 Solving -6.666666665 + x = -4.944132322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -4.944132322 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -4.944132322 + 6.666666665 x = -4.944132322 + 6.666666665 Combine like terms: -4.944132322 + 6.666666665 = 1.722534343 x = 1.722534343 Simplifying x = 1.722534343Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.610798987, 1.722534343}
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