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Simplifying 11x2 + -9x + -9 = 0 Reorder the terms: -9 + -9x + 11x2 = 0 Solving -9 + -9x + 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'. -0.8181818182 + -0.8181818182x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + -0.8181818182x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + -0.8181818182x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + -0.8181818182x + x2 = 0 + 0.8181818182 -0.8181818182x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 -0.8181818182x + x2 = 0.8181818182 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 = 0.8181818182 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182x + x2 = 0.8181818182 + 0.1673553719 Combine like terms: 0.8181818182 + 0.1673553719 = 0.9855371901 0.1673553719 + -0.8181818182x + x2 = 0.9855371901 Factor a perfect square on the left side: (x + -0.4090909091)(x + -0.4090909091) = 0.9855371901 Calculate the square root of the right side: 0.992742258 Break this problem into two subproblems by setting (x + -0.4090909091) equal to 0.992742258 and -0.992742258.Subproblem 1
x + -0.4090909091 = 0.992742258 Simplifying x + -0.4090909091 = 0.992742258 Reorder the terms: -0.4090909091 + x = 0.992742258 Solving -0.4090909091 + x = 0.992742258 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 = 0.992742258 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = 0.992742258 + 0.4090909091 x = 0.992742258 + 0.4090909091 Combine like terms: 0.992742258 + 0.4090909091 = 1.4018331671 x = 1.4018331671 Simplifying x = 1.4018331671Subproblem 2
x + -0.4090909091 = -0.992742258 Simplifying x + -0.4090909091 = -0.992742258 Reorder the terms: -0.4090909091 + x = -0.992742258 Solving -0.4090909091 + x = -0.992742258 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 = -0.992742258 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = -0.992742258 + 0.4090909091 x = -0.992742258 + 0.4090909091 Combine like terms: -0.992742258 + 0.4090909091 = -0.5836513489 x = -0.5836513489 Simplifying x = -0.5836513489Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4018331671, -0.5836513489}
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