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Simplifying 18x2 + -29x + -6 = 0 Reorder the terms: -6 + -29x + 18x2 = 0 Solving -6 + -29x + 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'. -0.3333333333 + -1.611111111x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -1.611111111x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -1.611111111x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -1.611111111x + x2 = 0 + 0.3333333333 -1.611111111x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -1.611111111x + x2 = 0.3333333333 The x term is -1.611111111x. Take half its coefficient (-0.8055555555). Square it (0.6489197530) and add it to both sides. Add '0.6489197530' to each side of the equation. -1.611111111x + 0.6489197530 + x2 = 0.3333333333 + 0.6489197530 Reorder the terms: 0.6489197530 + -1.611111111x + x2 = 0.3333333333 + 0.6489197530 Combine like terms: 0.3333333333 + 0.6489197530 = 0.9822530863 0.6489197530 + -1.611111111x + x2 = 0.9822530863 Factor a perfect square on the left side: (x + -0.8055555555)(x + -0.8055555555) = 0.9822530863 Calculate the square root of the right side: 0.991086821 Break this problem into two subproblems by setting (x + -0.8055555555) equal to 0.991086821 and -0.991086821.Subproblem 1
x + -0.8055555555 = 0.991086821 Simplifying x + -0.8055555555 = 0.991086821 Reorder the terms: -0.8055555555 + x = 0.991086821 Solving -0.8055555555 + x = 0.991086821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8055555555' to each side of the equation. -0.8055555555 + 0.8055555555 + x = 0.991086821 + 0.8055555555 Combine like terms: -0.8055555555 + 0.8055555555 = 0.0000000000 0.0000000000 + x = 0.991086821 + 0.8055555555 x = 0.991086821 + 0.8055555555 Combine like terms: 0.991086821 + 0.8055555555 = 1.7966423765 x = 1.7966423765 Simplifying x = 1.7966423765Subproblem 2
x + -0.8055555555 = -0.991086821 Simplifying x + -0.8055555555 = -0.991086821 Reorder the terms: -0.8055555555 + x = -0.991086821 Solving -0.8055555555 + x = -0.991086821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8055555555' to each side of the equation. -0.8055555555 + 0.8055555555 + x = -0.991086821 + 0.8055555555 Combine like terms: -0.8055555555 + 0.8055555555 = 0.0000000000 0.0000000000 + x = -0.991086821 + 0.8055555555 x = -0.991086821 + 0.8055555555 Combine like terms: -0.991086821 + 0.8055555555 = -0.1855312655 x = -0.1855312655 Simplifying x = -0.1855312655Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7966423765, -0.1855312655}
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