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Simplifying 3x2 + 30x + 40 = 0 Reorder the terms: 40 + 30x + 3x2 = 0 Solving 40 + 30x + 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 + 10x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + 10x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + 10x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + 10x + x2 = 0 + -13.33333333 10x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 10x + x2 = -13.33333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -13.33333333 + 25 Reorder the terms: 25 + 10x + x2 = -13.33333333 + 25 Combine like terms: -13.33333333 + 25 = 11.66666667 25 + 10x + x2 = 11.66666667 Factor a perfect square on the left side: (x + 5)(x + 5) = 11.66666667 Calculate the square root of the right side: 3.415650256 Break this problem into two subproblems by setting (x + 5) equal to 3.415650256 and -3.415650256.Subproblem 1
x + 5 = 3.415650256 Simplifying x + 5 = 3.415650256 Reorder the terms: 5 + x = 3.415650256 Solving 5 + x = 3.415650256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 3.415650256 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.415650256 + -5 x = 3.415650256 + -5 Combine like terms: 3.415650256 + -5 = -1.584349744 x = -1.584349744 Simplifying x = -1.584349744Subproblem 2
x + 5 = -3.415650256 Simplifying x + 5 = -3.415650256 Reorder the terms: 5 + x = -3.415650256 Solving 5 + x = -3.415650256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -3.415650256 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.415650256 + -5 x = -3.415650256 + -5 Combine like terms: -3.415650256 + -5 = -8.415650256 x = -8.415650256 Simplifying x = -8.415650256Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.584349744, -8.415650256}
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