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Simplifying 11x2 + 7x + -9 = 0 Reorder the terms: -9 + 7x + 11x2 = 0 Solving -9 + 7x + 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 + 0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 0.6363636364x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 0.6363636364x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 0.6363636364x + x2 = 0 + 0.8181818182 0.6363636364x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 0.6363636364x + x2 = 0.8181818182 The x term is 0.6363636364x. Take half its coefficient (0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. 0.6363636364x + 0.1012396694 + x2 = 0.8181818182 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364x + x2 = 0.8181818182 + 0.1012396694 Combine like terms: 0.8181818182 + 0.1012396694 = 0.9194214876 0.1012396694 + 0.6363636364x + x2 = 0.9194214876 Factor a perfect square on the left side: (x + 0.3181818182)(x + 0.3181818182) = 0.9194214876 Calculate the square root of the right side: 0.958864687 Break this problem into two subproblems by setting (x + 0.3181818182) equal to 0.958864687 and -0.958864687.Subproblem 1
x + 0.3181818182 = 0.958864687 Simplifying x + 0.3181818182 = 0.958864687 Reorder the terms: 0.3181818182 + x = 0.958864687 Solving 0.3181818182 + x = 0.958864687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + x = 0.958864687 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = 0.958864687 + -0.3181818182 x = 0.958864687 + -0.3181818182 Combine like terms: 0.958864687 + -0.3181818182 = 0.6406828688 x = 0.6406828688 Simplifying x = 0.6406828688Subproblem 2
x + 0.3181818182 = -0.958864687 Simplifying x + 0.3181818182 = -0.958864687 Reorder the terms: 0.3181818182 + x = -0.958864687 Solving 0.3181818182 + x = -0.958864687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + x = -0.958864687 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = -0.958864687 + -0.3181818182 x = -0.958864687 + -0.3181818182 Combine like terms: -0.958864687 + -0.3181818182 = -1.2770465052 x = -1.2770465052 Simplifying x = -1.2770465052Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6406828688, -1.2770465052}
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