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Simplifying 18x2 + -65x + -41 = 0 Reorder the terms: -41 + -65x + 18x2 = 0 Solving -41 + -65x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -2.277777778 + -3.611111111x + x2 = 0 Move the constant term to the right: Add '2.277777778' to each side of the equation. -2.277777778 + -3.611111111x + 2.277777778 + x2 = 0 + 2.277777778 Reorder the terms: -2.277777778 + 2.277777778 + -3.611111111x + x2 = 0 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + -3.611111111x + x2 = 0 + 2.277777778 -3.611111111x + x2 = 0 + 2.277777778 Combine like terms: 0 + 2.277777778 = 2.277777778 -3.611111111x + x2 = 2.277777778 The x term is -3.611111111x. Take half its coefficient (-1.805555556). Square it (3.260030866) and add it to both sides. Add '3.260030866' to each side of the equation. -3.611111111x + 3.260030866 + x2 = 2.277777778 + 3.260030866 Reorder the terms: 3.260030866 + -3.611111111x + x2 = 2.277777778 + 3.260030866 Combine like terms: 2.277777778 + 3.260030866 = 5.537808644 3.260030866 + -3.611111111x + x2 = 5.537808644 Factor a perfect square on the left side: (x + -1.805555556)(x + -1.805555556) = 5.537808644 Calculate the square root of the right side: 2.353254904 Break this problem into two subproblems by setting (x + -1.805555556) equal to 2.353254904 and -2.353254904.Subproblem 1
x + -1.805555556 = 2.353254904 Simplifying x + -1.805555556 = 2.353254904 Reorder the terms: -1.805555556 + x = 2.353254904 Solving -1.805555556 + x = 2.353254904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.805555556' to each side of the equation. -1.805555556 + 1.805555556 + x = 2.353254904 + 1.805555556 Combine like terms: -1.805555556 + 1.805555556 = 0.000000000 0.000000000 + x = 2.353254904 + 1.805555556 x = 2.353254904 + 1.805555556 Combine like terms: 2.353254904 + 1.805555556 = 4.15881046 x = 4.15881046 Simplifying x = 4.15881046Subproblem 2
x + -1.805555556 = -2.353254904 Simplifying x + -1.805555556 = -2.353254904 Reorder the terms: -1.805555556 + x = -2.353254904 Solving -1.805555556 + x = -2.353254904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.805555556' to each side of the equation. -1.805555556 + 1.805555556 + x = -2.353254904 + 1.805555556 Combine like terms: -1.805555556 + 1.805555556 = 0.000000000 0.000000000 + x = -2.353254904 + 1.805555556 x = -2.353254904 + 1.805555556 Combine like terms: -2.353254904 + 1.805555556 = -0.547699348 x = -0.547699348 Simplifying x = -0.547699348Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.15881046, -0.547699348}
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