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Simplifying 3x2 + -39x + 40 = 0 Reorder the terms: 40 + -39x + 3x2 = 0 Solving 40 + -39x + 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'. 13.33333333 + -13x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -13x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -13x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -13x + x2 = 0 + -13.33333333 -13x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -13x + x2 = -13.33333333 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -13.33333333 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -13.33333333 + 42.25 Combine like terms: -13.33333333 + 42.25 = 28.91666667 42.25 + -13x + x2 = 28.91666667 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 28.91666667 Calculate the square root of the right side: 5.377421935 Break this problem into two subproblems by setting (x + -6.5) equal to 5.377421935 and -5.377421935.Subproblem 1
x + -6.5 = 5.377421935 Simplifying x + -6.5 = 5.377421935 Reorder the terms: -6.5 + x = 5.377421935 Solving -6.5 + x = 5.377421935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 5.377421935 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.377421935 + 6.5 x = 5.377421935 + 6.5 Combine like terms: 5.377421935 + 6.5 = 11.877421935 x = 11.877421935 Simplifying x = 11.877421935Subproblem 2
x + -6.5 = -5.377421935 Simplifying x + -6.5 = -5.377421935 Reorder the terms: -6.5 + x = -5.377421935 Solving -6.5 + x = -5.377421935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -5.377421935 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.377421935 + 6.5 x = -5.377421935 + 6.5 Combine like terms: -5.377421935 + 6.5 = 1.122578065 x = 1.122578065 Simplifying x = 1.122578065Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.877421935, 1.122578065}
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