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Simplifying -22x2 + -33x + 18 = 0 Reorder the terms: 18 + -33x + -22x2 = 0 Solving 18 + -33x + -22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -22 the coefficient of the squared term: Divide each side by '-22'. -0.8181818182 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 1.5x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 1.5x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 1.5x + x2 = 0 + 0.8181818182 1.5x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 1.5x + x2 = 0.8181818182 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 = 0.8181818182 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.8181818182 + 0.5625 Combine like terms: 0.8181818182 + 0.5625 = 1.3806818182 0.5625 + 1.5x + x2 = 1.3806818182 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.3806818182 Calculate the square root of the right side: 1.175024178 Break this problem into two subproblems by setting (x + 0.75) equal to 1.175024178 and -1.175024178.Subproblem 1
x + 0.75 = 1.175024178 Simplifying x + 0.75 = 1.175024178 Reorder the terms: 0.75 + x = 1.175024178 Solving 0.75 + x = 1.175024178 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 = 1.175024178 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.175024178 + -0.75 x = 1.175024178 + -0.75 Combine like terms: 1.175024178 + -0.75 = 0.425024178 x = 0.425024178 Simplifying x = 0.425024178Subproblem 2
x + 0.75 = -1.175024178 Simplifying x + 0.75 = -1.175024178 Reorder the terms: 0.75 + x = -1.175024178 Solving 0.75 + x = -1.175024178 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 = -1.175024178 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.175024178 + -0.75 x = -1.175024178 + -0.75 Combine like terms: -1.175024178 + -0.75 = -1.925024178 x = -1.925024178 Simplifying x = -1.925024178Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.425024178, -1.925024178}
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