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Simplifying 11x2 + -3x + 2 = 121 Reorder the terms: 2 + -3x + 11x2 = 121 Solving 2 + -3x + 11x2 = 121 Solving for variable 'x'. Reorder the terms: 2 + -121 + -3x + 11x2 = 121 + -121 Combine like terms: 2 + -121 = -119 -119 + -3x + 11x2 = 121 + -121 Combine like terms: 121 + -121 = 0 -119 + -3x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -10.81818182 + -0.2727272727x + x2 = 0 Move the constant term to the right: Add '10.81818182' to each side of the equation. -10.81818182 + -0.2727272727x + 10.81818182 + x2 = 0 + 10.81818182 Reorder the terms: -10.81818182 + 10.81818182 + -0.2727272727x + x2 = 0 + 10.81818182 Combine like terms: -10.81818182 + 10.81818182 = 0.00000000 0.00000000 + -0.2727272727x + x2 = 0 + 10.81818182 -0.2727272727x + x2 = 0 + 10.81818182 Combine like terms: 0 + 10.81818182 = 10.81818182 -0.2727272727x + x2 = 10.81818182 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 = 10.81818182 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727x + x2 = 10.81818182 + 0.01859504133 Combine like terms: 10.81818182 + 0.01859504133 = 10.83677686133 0.01859504133 + -0.2727272727x + x2 = 10.83677686133 Factor a perfect square on the left side: (x + -0.1363636364)(x + -0.1363636364) = 10.83677686133 Calculate the square root of the right side: 3.291926011 Break this problem into two subproblems by setting (x + -0.1363636364) equal to 3.291926011 and -3.291926011.Subproblem 1
x + -0.1363636364 = 3.291926011 Simplifying x + -0.1363636364 = 3.291926011 Reorder the terms: -0.1363636364 + x = 3.291926011 Solving -0.1363636364 + x = 3.291926011 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 = 3.291926011 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = 3.291926011 + 0.1363636364 x = 3.291926011 + 0.1363636364 Combine like terms: 3.291926011 + 0.1363636364 = 3.4282896474 x = 3.4282896474 Simplifying x = 3.4282896474Subproblem 2
x + -0.1363636364 = -3.291926011 Simplifying x + -0.1363636364 = -3.291926011 Reorder the terms: -0.1363636364 + x = -3.291926011 Solving -0.1363636364 + x = -3.291926011 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 = -3.291926011 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = -3.291926011 + 0.1363636364 x = -3.291926011 + 0.1363636364 Combine like terms: -3.291926011 + 0.1363636364 = -3.1555623746 x = -3.1555623746 Simplifying x = -3.1555623746Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4282896474, -3.1555623746}
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