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Simplifying 3x2 + 125x + 1 = 0 Reorder the terms: 1 + 125x + 3x2 = 0 Solving 1 + 125x + 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'. 0.3333333333 + 41.66666667x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 41.66666667x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 41.66666667x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 41.66666667x + x2 = 0 + -0.3333333333 41.66666667x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 41.66666667x + x2 = -0.3333333333 The x term is 41.66666667x. Take half its coefficient (20.83333334). Square it (434.0277781) and add it to both sides. Add '434.0277781' to each side of the equation. 41.66666667x + 434.0277781 + x2 = -0.3333333333 + 434.0277781 Reorder the terms: 434.0277781 + 41.66666667x + x2 = -0.3333333333 + 434.0277781 Combine like terms: -0.3333333333 + 434.0277781 = 433.6944447667 434.0277781 + 41.66666667x + x2 = 433.6944447667 Factor a perfect square on the left side: (x + 20.83333334)(x + 20.83333334) = 433.6944447667 Calculate the square root of the right side: 20.825331804 Break this problem into two subproblems by setting (x + 20.83333334) equal to 20.825331804 and -20.825331804.Subproblem 1
x + 20.83333334 = 20.825331804 Simplifying x + 20.83333334 = 20.825331804 Reorder the terms: 20.83333334 + x = 20.825331804 Solving 20.83333334 + x = 20.825331804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.83333334' to each side of the equation. 20.83333334 + -20.83333334 + x = 20.825331804 + -20.83333334 Combine like terms: 20.83333334 + -20.83333334 = 0.00000000 0.00000000 + x = 20.825331804 + -20.83333334 x = 20.825331804 + -20.83333334 Combine like terms: 20.825331804 + -20.83333334 = -0.008001536 x = -0.008001536 Simplifying x = -0.008001536Subproblem 2
x + 20.83333334 = -20.825331804 Simplifying x + 20.83333334 = -20.825331804 Reorder the terms: 20.83333334 + x = -20.825331804 Solving 20.83333334 + x = -20.825331804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.83333334' to each side of the equation. 20.83333334 + -20.83333334 + x = -20.825331804 + -20.83333334 Combine like terms: 20.83333334 + -20.83333334 = 0.00000000 0.00000000 + x = -20.825331804 + -20.83333334 x = -20.825331804 + -20.83333334 Combine like terms: -20.825331804 + -20.83333334 = -41.658665144 x = -41.658665144 Simplifying x = -41.658665144Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.008001536, -41.658665144}
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