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Simplifying 11x2 + 3x + -18 = 0 Reorder the terms: -18 + 3x + 11x2 = 0 Solving -18 + 3x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.636363636 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + 0.2727272727x + 1.636363636 + x2 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + 0.2727272727x + x2 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + 0.2727272727x + x2 = 0 + 1.636363636 0.2727272727x + x2 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 0.2727272727x + x2 = 1.636363636 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 1.636363636 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 1.636363636 + 0.01859504133 Combine like terms: 1.636363636 + 0.01859504133 = 1.65495867733 0.01859504133 + 0.2727272727x + x2 = 1.65495867733 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 1.65495867733 Calculate the square root of the right side: 1.286451972 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 1.286451972 and -1.286451972.Subproblem 1
x + 0.1363636364 = 1.286451972 Simplifying x + 0.1363636364 = 1.286451972 Reorder the terms: 0.1363636364 + x = 1.286451972 Solving 0.1363636364 + x = 1.286451972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 1.286451972 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 1.286451972 + -0.1363636364 x = 1.286451972 + -0.1363636364 Combine like terms: 1.286451972 + -0.1363636364 = 1.1500883356 x = 1.1500883356 Simplifying x = 1.1500883356Subproblem 2
x + 0.1363636364 = -1.286451972 Simplifying x + 0.1363636364 = -1.286451972 Reorder the terms: 0.1363636364 + x = -1.286451972 Solving 0.1363636364 + x = -1.286451972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -1.286451972 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -1.286451972 + -0.1363636364 x = -1.286451972 + -0.1363636364 Combine like terms: -1.286451972 + -0.1363636364 = -1.4228156084 x = -1.4228156084 Simplifying x = -1.4228156084Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1500883356, -1.4228156084}
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