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Simplifying 18x2 + 13x + -41 = 0 Reorder the terms: -41 + 13x + 18x2 = 0 Solving -41 + 13x + 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 + 0.7222222222x + x2 = 0 Move the constant term to the right: Add '2.277777778' to each side of the equation. -2.277777778 + 0.7222222222x + 2.277777778 + x2 = 0 + 2.277777778 Reorder the terms: -2.277777778 + 2.277777778 + 0.7222222222x + x2 = 0 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + 0.7222222222x + x2 = 0 + 2.277777778 0.7222222222x + x2 = 0 + 2.277777778 Combine like terms: 0 + 2.277777778 = 2.277777778 0.7222222222x + x2 = 2.277777778 The x term is 0.7222222222x. Take half its coefficient (0.3611111111). Square it (0.1304012346) and add it to both sides. Add '0.1304012346' to each side of the equation. 0.7222222222x + 0.1304012346 + x2 = 2.277777778 + 0.1304012346 Reorder the terms: 0.1304012346 + 0.7222222222x + x2 = 2.277777778 + 0.1304012346 Combine like terms: 2.277777778 + 0.1304012346 = 2.4081790126 0.1304012346 + 0.7222222222x + x2 = 2.4081790126 Factor a perfect square on the left side: (x + 0.3611111111)(x + 0.3611111111) = 2.4081790126 Calculate the square root of the right side: 1.551830858 Break this problem into two subproblems by setting (x + 0.3611111111) equal to 1.551830858 and -1.551830858.Subproblem 1
x + 0.3611111111 = 1.551830858 Simplifying x + 0.3611111111 = 1.551830858 Reorder the terms: 0.3611111111 + x = 1.551830858 Solving 0.3611111111 + x = 1.551830858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3611111111' to each side of the equation. 0.3611111111 + -0.3611111111 + x = 1.551830858 + -0.3611111111 Combine like terms: 0.3611111111 + -0.3611111111 = 0.0000000000 0.0000000000 + x = 1.551830858 + -0.3611111111 x = 1.551830858 + -0.3611111111 Combine like terms: 1.551830858 + -0.3611111111 = 1.1907197469 x = 1.1907197469 Simplifying x = 1.1907197469Subproblem 2
x + 0.3611111111 = -1.551830858 Simplifying x + 0.3611111111 = -1.551830858 Reorder the terms: 0.3611111111 + x = -1.551830858 Solving 0.3611111111 + x = -1.551830858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3611111111' to each side of the equation. 0.3611111111 + -0.3611111111 + x = -1.551830858 + -0.3611111111 Combine like terms: 0.3611111111 + -0.3611111111 = 0.0000000000 0.0000000000 + x = -1.551830858 + -0.3611111111 x = -1.551830858 + -0.3611111111 Combine like terms: -1.551830858 + -0.3611111111 = -1.9129419691 x = -1.9129419691 Simplifying x = -1.9129419691Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1907197469, -1.9129419691}
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