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Simplifying 12x2 + -41x + 18 = 0 Reorder the terms: 18 + -41x + 12x2 = 0 Solving 18 + -41x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.5 + -3.416666667x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.416666667x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.416666667x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.416666667x + x2 = 0 + -1.5 -3.416666667x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.416666667x + x2 = -1.5 The x term is -3.416666667x. Take half its coefficient (-1.708333334). Square it (2.918402780) and add it to both sides. Add '2.918402780' to each side of the equation. -3.416666667x + 2.918402780 + x2 = -1.5 + 2.918402780 Reorder the terms: 2.918402780 + -3.416666667x + x2 = -1.5 + 2.918402780 Combine like terms: -1.5 + 2.918402780 = 1.41840278 2.918402780 + -3.416666667x + x2 = 1.41840278 Factor a perfect square on the left side: (x + -1.708333334)(x + -1.708333334) = 1.41840278 Calculate the square root of the right side: 1.190967162 Break this problem into two subproblems by setting (x + -1.708333334) equal to 1.190967162 and -1.190967162.Subproblem 1
x + -1.708333334 = 1.190967162 Simplifying x + -1.708333334 = 1.190967162 Reorder the terms: -1.708333334 + x = 1.190967162 Solving -1.708333334 + x = 1.190967162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.708333334' to each side of the equation. -1.708333334 + 1.708333334 + x = 1.190967162 + 1.708333334 Combine like terms: -1.708333334 + 1.708333334 = 0.000000000 0.000000000 + x = 1.190967162 + 1.708333334 x = 1.190967162 + 1.708333334 Combine like terms: 1.190967162 + 1.708333334 = 2.899300496 x = 2.899300496 Simplifying x = 2.899300496Subproblem 2
x + -1.708333334 = -1.190967162 Simplifying x + -1.708333334 = -1.190967162 Reorder the terms: -1.708333334 + x = -1.190967162 Solving -1.708333334 + x = -1.190967162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.708333334' to each side of the equation. -1.708333334 + 1.708333334 + x = -1.190967162 + 1.708333334 Combine like terms: -1.708333334 + 1.708333334 = 0.000000000 0.000000000 + x = -1.190967162 + 1.708333334 x = -1.190967162 + 1.708333334 Combine like terms: -1.190967162 + 1.708333334 = 0.517366172 x = 0.517366172 Simplifying x = 0.517366172Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.899300496, 0.517366172}
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