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Simplifying 3x2 + -12x + -40 = 0 Reorder the terms: -40 + -12x + 3x2 = 0 Solving -40 + -12x + 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 + -4x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -4x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -4x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -4x + x2 = 0 + 13.33333333 -4x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -4x + x2 = 13.33333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 13.33333333 + 4 Reorder the terms: 4 + -4x + x2 = 13.33333333 + 4 Combine like terms: 13.33333333 + 4 = 17.33333333 4 + -4x + x2 = 17.33333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 17.33333333 Calculate the square root of the right side: 4.163331999 Break this problem into two subproblems by setting (x + -2) equal to 4.163331999 and -4.163331999.Subproblem 1
x + -2 = 4.163331999 Simplifying x + -2 = 4.163331999 Reorder the terms: -2 + x = 4.163331999 Solving -2 + x = 4.163331999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.163331999 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.163331999 + 2 x = 4.163331999 + 2 Combine like terms: 4.163331999 + 2 = 6.163331999 x = 6.163331999 Simplifying x = 6.163331999Subproblem 2
x + -2 = -4.163331999 Simplifying x + -2 = -4.163331999 Reorder the terms: -2 + x = -4.163331999 Solving -2 + x = -4.163331999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.163331999 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.163331999 + 2 x = -4.163331999 + 2 Combine like terms: -4.163331999 + 2 = -2.163331999 x = -2.163331999 Simplifying x = -2.163331999Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.163331999, -2.163331999}
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