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Simplifying 2x2 + -18x + 41 = x2 Reorder the terms: 41 + -18x + 2x2 = x2 Solving 41 + -18x + 2x2 = x2 Solving for variable 'x'. Combine like terms: 2x2 + -1x2 = 1x2 41 + -18x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 41 + -18x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -18x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -18x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -18x + x2 = 0 + -41 -18x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -18x + x2 = -41 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -41 + 81 Reorder the terms: 81 + -18x + x2 = -41 + 81 Combine like terms: -41 + 81 = 40 81 + -18x + x2 = 40 Factor a perfect square on the left side: (x + -9)(x + -9) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -9) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -9 = 6.32455532 Simplifying x + -9 = 6.32455532 Reorder the terms: -9 + x = 6.32455532 Solving -9 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 6.32455532 + 9 Combine like terms: -9 + 9 = 0 0 + x = 6.32455532 + 9 x = 6.32455532 + 9 Combine like terms: 6.32455532 + 9 = 15.32455532 x = 15.32455532 Simplifying x = 15.32455532Subproblem 2
x + -9 = -6.32455532 Simplifying x + -9 = -6.32455532 Reorder the terms: -9 + x = -6.32455532 Solving -9 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -6.32455532 + 9 Combine like terms: -9 + 9 = 0 0 + x = -6.32455532 + 9 x = -6.32455532 + 9 Combine like terms: -6.32455532 + 9 = 2.67544468 x = 2.67544468 Simplifying x = 2.67544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.32455532, 2.67544468}
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