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Simplifying -22x2 + -18x + 9 = 0 Reorder the terms: 9 + -18x + -22x2 = 0 Solving 9 + -18x + -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'. -0.4090909091 + 0.8181818182x + x2 = 0 Move the constant term to the right: Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.8181818182x + 0.4090909091 + x2 = 0 + 0.4090909091 Reorder the terms: -0.4090909091 + 0.4090909091 + 0.8181818182x + x2 = 0 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + 0.8181818182x + x2 = 0 + 0.4090909091 0.8181818182x + x2 = 0 + 0.4090909091 Combine like terms: 0 + 0.4090909091 = 0.4090909091 0.8181818182x + x2 = 0.4090909091 The x term is 0.8181818182x. Take half its coefficient (0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. 0.8181818182x + 0.1673553719 + x2 = 0.4090909091 + 0.1673553719 Reorder the terms: 0.1673553719 + 0.8181818182x + x2 = 0.4090909091 + 0.1673553719 Combine like terms: 0.4090909091 + 0.1673553719 = 0.576446281 0.1673553719 + 0.8181818182x + x2 = 0.576446281 Factor a perfect square on the left side: (x + 0.4090909091)(x + 0.4090909091) = 0.576446281 Calculate the square root of the right side: 0.759240595 Break this problem into two subproblems by setting (x + 0.4090909091) equal to 0.759240595 and -0.759240595.Subproblem 1
x + 0.4090909091 = 0.759240595 Simplifying x + 0.4090909091 = 0.759240595 Reorder the terms: 0.4090909091 + x = 0.759240595 Solving 0.4090909091 + x = 0.759240595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + x = 0.759240595 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + x = 0.759240595 + -0.4090909091 x = 0.759240595 + -0.4090909091 Combine like terms: 0.759240595 + -0.4090909091 = 0.3501496859 x = 0.3501496859 Simplifying x = 0.3501496859Subproblem 2
x + 0.4090909091 = -0.759240595 Simplifying x + 0.4090909091 = -0.759240595 Reorder the terms: 0.4090909091 + x = -0.759240595 Solving 0.4090909091 + x = -0.759240595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + x = -0.759240595 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + x = -0.759240595 + -0.4090909091 x = -0.759240595 + -0.4090909091 Combine like terms: -0.759240595 + -0.4090909091 = -1.1683315041 x = -1.1683315041 Simplifying x = -1.1683315041Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3501496859, -1.1683315041}
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