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Simplifying 0.11x2 + -3x + 9 = 0 Reorder the terms: 9 + -3x + 0.11x2 = 0 Solving 9 + -3x + 0.11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.11 the coefficient of the squared term: Divide each side by '0.11'. 81.81818182 + -27.27272727x + x2 = 0 Move the constant term to the right: Add '-81.81818182' to each side of the equation. 81.81818182 + -27.27272727x + -81.81818182 + x2 = 0 + -81.81818182 Reorder the terms: 81.81818182 + -81.81818182 + -27.27272727x + x2 = 0 + -81.81818182 Combine like terms: 81.81818182 + -81.81818182 = 0.00000000 0.00000000 + -27.27272727x + x2 = 0 + -81.81818182 -27.27272727x + x2 = 0 + -81.81818182 Combine like terms: 0 + -81.81818182 = -81.81818182 -27.27272727x + x2 = -81.81818182 The x term is -27.27272727x. Take half its coefficient (-13.63636364). Square it (185.9504133) and add it to both sides. Add '185.9504133' to each side of the equation. -27.27272727x + 185.9504133 + x2 = -81.81818182 + 185.9504133 Reorder the terms: 185.9504133 + -27.27272727x + x2 = -81.81818182 + 185.9504133 Combine like terms: -81.81818182 + 185.9504133 = 104.13223148 185.9504133 + -27.27272727x + x2 = 104.13223148 Factor a perfect square on the left side: (x + -13.63636364)(x + -13.63636364) = 104.13223148 Calculate the square root of the right side: 10.204520149 Break this problem into two subproblems by setting (x + -13.63636364) equal to 10.204520149 and -10.204520149.Subproblem 1
x + -13.63636364 = 10.204520149 Simplifying x + -13.63636364 = 10.204520149 Reorder the terms: -13.63636364 + x = 10.204520149 Solving -13.63636364 + x = 10.204520149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.63636364' to each side of the equation. -13.63636364 + 13.63636364 + x = 10.204520149 + 13.63636364 Combine like terms: -13.63636364 + 13.63636364 = 0.00000000 0.00000000 + x = 10.204520149 + 13.63636364 x = 10.204520149 + 13.63636364 Combine like terms: 10.204520149 + 13.63636364 = 23.840883789 x = 23.840883789 Simplifying x = 23.840883789Subproblem 2
x + -13.63636364 = -10.204520149 Simplifying x + -13.63636364 = -10.204520149 Reorder the terms: -13.63636364 + x = -10.204520149 Solving -13.63636364 + x = -10.204520149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.63636364' to each side of the equation. -13.63636364 + 13.63636364 + x = -10.204520149 + 13.63636364 Combine like terms: -13.63636364 + 13.63636364 = 0.00000000 0.00000000 + x = -10.204520149 + 13.63636364 x = -10.204520149 + 13.63636364 Combine like terms: -10.204520149 + 13.63636364 = 3.431843491 x = 3.431843491 Simplifying x = 3.431843491Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.840883789, 3.431843491}
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