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Simplifying 12x2 + 18x + -41 = 0 Reorder the terms: -41 + 18x + 12x2 = 0 Solving -41 + 18x + 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'. -3.416666667 + 1.5x + x2 = 0 Move the constant term to the right: Add '3.416666667' to each side of the equation. -3.416666667 + 1.5x + 3.416666667 + x2 = 0 + 3.416666667 Reorder the terms: -3.416666667 + 3.416666667 + 1.5x + x2 = 0 + 3.416666667 Combine like terms: -3.416666667 + 3.416666667 = 0.000000000 0.000000000 + 1.5x + x2 = 0 + 3.416666667 1.5x + x2 = 0 + 3.416666667 Combine like terms: 0 + 3.416666667 = 3.416666667 1.5x + x2 = 3.416666667 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 3.416666667 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3.416666667 + 0.5625 Combine like terms: 3.416666667 + 0.5625 = 3.979166667 0.5625 + 1.5x + x2 = 3.979166667 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 3.979166667 Calculate the square root of the right side: 1.994784867 Break this problem into two subproblems by setting (x + 0.75) equal to 1.994784867 and -1.994784867.Subproblem 1
x + 0.75 = 1.994784867 Simplifying x + 0.75 = 1.994784867 Reorder the terms: 0.75 + x = 1.994784867 Solving 0.75 + x = 1.994784867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.994784867 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.994784867 + -0.75 x = 1.994784867 + -0.75 Combine like terms: 1.994784867 + -0.75 = 1.244784867 x = 1.244784867 Simplifying x = 1.244784867Subproblem 2
x + 0.75 = -1.994784867 Simplifying x + 0.75 = -1.994784867 Reorder the terms: 0.75 + x = -1.994784867 Solving 0.75 + x = -1.994784867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.994784867 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.994784867 + -0.75 x = -1.994784867 + -0.75 Combine like terms: -1.994784867 + -0.75 = -2.744784867 x = -2.744784867 Simplifying x = -2.744784867Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.244784867, -2.744784867}
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