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Simplifying 22x2 + 11x = 0.01 Reorder the terms: 11x + 22x2 = 0.01 Solving 11x + 22x2 = 0.01 Solving for variable 'x'. Reorder the terms: -0.01 + 11x + 22x2 = 0.01 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 -0.01 + 11x + 22x2 = 0.00 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.0004545454545 + 0.5x + x2 = 0.00 Move the constant term to the right: Add '0.0004545454545' to each side of the equation. -0.0004545454545 + 0.5x + 0.0004545454545 + x2 = 0.00 + 0.0004545454545 Reorder the terms: -0.0004545454545 + 0.0004545454545 + 0.5x + x2 = 0.00 + 0.0004545454545 Combine like terms: -0.0004545454545 + 0.0004545454545 = 0.0000000000000 0.0000000000000 + 0.5x + x2 = 0.00 + 0.0004545454545 0.5x + x2 = 0.00 + 0.0004545454545 Combine like terms: 0.00 + 0.0004545454545 = 0.0004545454545 0.5x + x2 = 0.0004545454545 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.0004545454545 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.0004545454545 + 0.0625 Combine like terms: 0.0004545454545 + 0.0625 = 0.0629545454545 0.0625 + 0.5x + x2 = 0.0629545454545 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.0629545454545 Calculate the square root of the right side: 0.250907444 Break this problem into two subproblems by setting (x + 0.25) equal to 0.250907444 and -0.250907444.Subproblem 1
x + 0.25 = 0.250907444 Simplifying x + 0.25 = 0.250907444 Reorder the terms: 0.25 + x = 0.250907444 Solving 0.25 + x = 0.250907444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.250907444 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.250907444 + -0.25 x = 0.250907444 + -0.25 Combine like terms: 0.250907444 + -0.25 = 0.000907444 x = 0.000907444 Simplifying x = 0.000907444Subproblem 2
x + 0.25 = -0.250907444 Simplifying x + 0.25 = -0.250907444 Reorder the terms: 0.25 + x = -0.250907444 Solving 0.25 + x = -0.250907444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.250907444 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.250907444 + -0.25 x = -0.250907444 + -0.25 Combine like terms: -0.250907444 + -0.25 = -0.500907444 x = -0.500907444 Simplifying x = -0.500907444Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000907444, -0.500907444}
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