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Simplifying -1(18x2 + 4x + -11) = 0 Reorder the terms: -1(-11 + 4x + 18x2) = 0 (-11 * -1 + 4x * -1 + 18x2 * -1) = 0 (11 + -4x + -18x2) = 0 Solving 11 + -4x + -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'. -0.6111111111 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.6111111111' to each side of the equation. -0.6111111111 + 0.2222222222x + 0.6111111111 + x2 = 0 + 0.6111111111 Reorder the terms: -0.6111111111 + 0.6111111111 + 0.2222222222x + x2 = 0 + 0.6111111111 Combine like terms: -0.6111111111 + 0.6111111111 = 0.0000000000 0.0000000000 + 0.2222222222x + x2 = 0 + 0.6111111111 0.2222222222x + x2 = 0 + 0.6111111111 Combine like terms: 0 + 0.6111111111 = 0.6111111111 0.2222222222x + x2 = 0.6111111111 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 0.6111111111 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.6111111111 + 0.01234567901 Combine like terms: 0.6111111111 + 0.01234567901 = 0.62345679011 0.01234567901 + 0.2222222222x + x2 = 0.62345679011 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.62345679011 Calculate the square root of the right side: 0.7895928 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.7895928 and -0.7895928.Subproblem 1
x + 0.1111111111 = 0.7895928 Simplifying x + 0.1111111111 = 0.7895928 Reorder the terms: 0.1111111111 + x = 0.7895928 Solving 0.1111111111 + x = 0.7895928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 0.7895928 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.7895928 + -0.1111111111 x = 0.7895928 + -0.1111111111 Combine like terms: 0.7895928 + -0.1111111111 = 0.6784816889 x = 0.6784816889 Simplifying x = 0.6784816889Subproblem 2
x + 0.1111111111 = -0.7895928 Simplifying x + 0.1111111111 = -0.7895928 Reorder the terms: 0.1111111111 + x = -0.7895928 Solving 0.1111111111 + x = -0.7895928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -0.7895928 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.7895928 + -0.1111111111 x = -0.7895928 + -0.1111111111 Combine like terms: -0.7895928 + -0.1111111111 = -0.9007039111 x = -0.9007039111 Simplifying x = -0.9007039111Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6784816889, -0.9007039111}
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