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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 = 2.163331999 x = 2.163331999 Simplifying x = 2.163331999Subproblem 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 = -6.163331999 x = -6.163331999 Simplifying x = -6.163331999Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.163331999, -6.163331999}
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