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Simplifying 0.0855x2 + -0.932x + 1.773 = 0 Reorder the terms: 1.773 + -0.932x + 0.0855x2 = 0 Solving 1.773 + -0.932x + 0.0855x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0855 the coefficient of the squared term: Divide each side by '0.0855'. 20.73684211 + -10.9005848x + x2 = 0 Move the constant term to the right: Add '-20.73684211' to each side of the equation. 20.73684211 + -10.9005848x + -20.73684211 + x2 = 0 + -20.73684211 Reorder the terms: 20.73684211 + -20.73684211 + -10.9005848x + x2 = 0 + -20.73684211 Combine like terms: 20.73684211 + -20.73684211 = 0.00000000 0.00000000 + -10.9005848x + x2 = 0 + -20.73684211 -10.9005848x + x2 = 0 + -20.73684211 Combine like terms: 0 + -20.73684211 = -20.73684211 -10.9005848x + x2 = -20.73684211 The x term is -10.9005848x. Take half its coefficient (-5.4502924). Square it (29.70568725) and add it to both sides. Add '29.70568725' to each side of the equation. -10.9005848x + 29.70568725 + x2 = -20.73684211 + 29.70568725 Reorder the terms: 29.70568725 + -10.9005848x + x2 = -20.73684211 + 29.70568725 Combine like terms: -20.73684211 + 29.70568725 = 8.96884514 29.70568725 + -10.9005848x + x2 = 8.96884514 Factor a perfect square on the left side: (x + -5.4502924)(x + -5.4502924) = 8.96884514 Calculate the square root of the right side: 2.994803022 Break this problem into two subproblems by setting (x + -5.4502924) equal to 2.994803022 and -2.994803022.Subproblem 1
x + -5.4502924 = 2.994803022 Simplifying x + -5.4502924 = 2.994803022 Reorder the terms: -5.4502924 + x = 2.994803022 Solving -5.4502924 + x = 2.994803022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.4502924' to each side of the equation. -5.4502924 + 5.4502924 + x = 2.994803022 + 5.4502924 Combine like terms: -5.4502924 + 5.4502924 = 0.0000000 0.0000000 + x = 2.994803022 + 5.4502924 x = 2.994803022 + 5.4502924 Combine like terms: 2.994803022 + 5.4502924 = 8.445095422 x = 8.445095422 Simplifying x = 8.445095422Subproblem 2
x + -5.4502924 = -2.994803022 Simplifying x + -5.4502924 = -2.994803022 Reorder the terms: -5.4502924 + x = -2.994803022 Solving -5.4502924 + x = -2.994803022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.4502924' to each side of the equation. -5.4502924 + 5.4502924 + x = -2.994803022 + 5.4502924 Combine like terms: -5.4502924 + 5.4502924 = 0.0000000 0.0000000 + x = -2.994803022 + 5.4502924 x = -2.994803022 + 5.4502924 Combine like terms: -2.994803022 + 5.4502924 = 2.455489378 x = 2.455489378 Simplifying x = 2.455489378Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.445095422, 2.455489378}
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