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Simplifying 11x2 + 3x + -9 = 0 Reorder the terms: -9 + 3x + 11x2 = 0 Solving -9 + 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'. -0.8181818182 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 0.2727272727x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 0.2727272727x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 0.2727272727x + x2 = 0 + 0.8181818182 0.2727272727x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 0.2727272727x + x2 = 0.8181818182 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 = 0.8181818182 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 0.8181818182 + 0.01859504133 Combine like terms: 0.8181818182 + 0.01859504133 = 0.83677685953 0.01859504133 + 0.2727272727x + x2 = 0.83677685953 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 0.83677685953 Calculate the square root of the right side: 0.914755082 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 0.914755082 and -0.914755082.Subproblem 1
x + 0.1363636364 = 0.914755082 Simplifying x + 0.1363636364 = 0.914755082 Reorder the terms: 0.1363636364 + x = 0.914755082 Solving 0.1363636364 + x = 0.914755082 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 = 0.914755082 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 0.914755082 + -0.1363636364 x = 0.914755082 + -0.1363636364 Combine like terms: 0.914755082 + -0.1363636364 = 0.7783914456 x = 0.7783914456 Simplifying x = 0.7783914456Subproblem 2
x + 0.1363636364 = -0.914755082 Simplifying x + 0.1363636364 = -0.914755082 Reorder the terms: 0.1363636364 + x = -0.914755082 Solving 0.1363636364 + x = -0.914755082 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 = -0.914755082 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -0.914755082 + -0.1363636364 x = -0.914755082 + -0.1363636364 Combine like terms: -0.914755082 + -0.1363636364 = -1.0511187184 x = -1.0511187184 Simplifying x = -1.0511187184Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7783914456, -1.0511187184}
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