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Simplifying 11x2 + -22.4x + 1.44 = 0 Reorder the terms: 1.44 + -22.4x + 11x2 = 0 Solving 1.44 + -22.4x + 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'. 0.1309090909 + -2.036363636x + x2 = 0 Move the constant term to the right: Add '-0.1309090909' to each side of the equation. 0.1309090909 + -2.036363636x + -0.1309090909 + x2 = 0 + -0.1309090909 Reorder the terms: 0.1309090909 + -0.1309090909 + -2.036363636x + x2 = 0 + -0.1309090909 Combine like terms: 0.1309090909 + -0.1309090909 = 0.0000000000 0.0000000000 + -2.036363636x + x2 = 0 + -0.1309090909 -2.036363636x + x2 = 0 + -0.1309090909 Combine like terms: 0 + -0.1309090909 = -0.1309090909 -2.036363636x + x2 = -0.1309090909 The x term is -2.036363636x. Take half its coefficient (-1.018181818). Square it (1.036694215) and add it to both sides. Add '1.036694215' to each side of the equation. -2.036363636x + 1.036694215 + x2 = -0.1309090909 + 1.036694215 Reorder the terms: 1.036694215 + -2.036363636x + x2 = -0.1309090909 + 1.036694215 Combine like terms: -0.1309090909 + 1.036694215 = 0.9057851241 1.036694215 + -2.036363636x + x2 = 0.9057851241 Factor a perfect square on the left side: (x + -1.018181818)(x + -1.018181818) = 0.9057851241 Calculate the square root of the right side: 0.951727442 Break this problem into two subproblems by setting (x + -1.018181818) equal to 0.951727442 and -0.951727442.Subproblem 1
x + -1.018181818 = 0.951727442 Simplifying x + -1.018181818 = 0.951727442 Reorder the terms: -1.018181818 + x = 0.951727442 Solving -1.018181818 + x = 0.951727442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.018181818' to each side of the equation. -1.018181818 + 1.018181818 + x = 0.951727442 + 1.018181818 Combine like terms: -1.018181818 + 1.018181818 = 0.000000000 0.000000000 + x = 0.951727442 + 1.018181818 x = 0.951727442 + 1.018181818 Combine like terms: 0.951727442 + 1.018181818 = 1.96990926 x = 1.96990926 Simplifying x = 1.96990926Subproblem 2
x + -1.018181818 = -0.951727442 Simplifying x + -1.018181818 = -0.951727442 Reorder the terms: -1.018181818 + x = -0.951727442 Solving -1.018181818 + x = -0.951727442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.018181818' to each side of the equation. -1.018181818 + 1.018181818 + x = -0.951727442 + 1.018181818 Combine like terms: -1.018181818 + 1.018181818 = 0.000000000 0.000000000 + x = -0.951727442 + 1.018181818 x = -0.951727442 + 1.018181818 Combine like terms: -0.951727442 + 1.018181818 = 0.066454376 x = 0.066454376 Simplifying x = 0.066454376Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.96990926, 0.066454376}
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