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Simplifying 1.21x2 + 2.64x + 1.44 = 0 Reorder the terms: 1.44 + 2.64x + 1.21x2 = 0 Solving 1.44 + 2.64x + 1.21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.21 the coefficient of the squared term: Divide each side by '1.21'. 1.190082645 + 2.181818182x + x2 = 0 Move the constant term to the right: Add '-1.190082645' to each side of the equation. 1.190082645 + 2.181818182x + -1.190082645 + x2 = 0 + -1.190082645 Reorder the terms: 1.190082645 + -1.190082645 + 2.181818182x + x2 = 0 + -1.190082645 Combine like terms: 1.190082645 + -1.190082645 = 0.000000000 0.000000000 + 2.181818182x + x2 = 0 + -1.190082645 2.181818182x + x2 = 0 + -1.190082645 Combine like terms: 0 + -1.190082645 = -1.190082645 2.181818182x + x2 = -1.190082645 The x term is 2.181818182x. Take half its coefficient (1.090909091). Square it (1.190082645) and add it to both sides. Add '1.190082645' to each side of the equation. 2.181818182x + 1.190082645 + x2 = -1.190082645 + 1.190082645 Reorder the terms: 1.190082645 + 2.181818182x + x2 = -1.190082645 + 1.190082645 Combine like terms: -1.190082645 + 1.190082645 = 0.000000000 1.190082645 + 2.181818182x + x2 = 0.000000000 Factor a perfect square on the left side: (x + 1.090909091)(x + 1.090909091) = 0.000000000 Calculate the square root of the right side: 0.000000000 Break this problem into two subproblems by setting (x + 1.090909091) equal to 0.000000000 and 0.000000000.Subproblem 1
x + 1.090909091 = 0.000000000 Simplifying x + 1.090909091 = 0.000000000 Reorder the terms: 1.090909091 + x = 0.000000000 Solving 1.090909091 + x = 0.000000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.090909091' to each side of the equation. 1.090909091 + -1.090909091 + x = 0.000000000 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + x = 0.000000000 + -1.090909091 x = 0.000000000 + -1.090909091 Combine like terms: 0.000000000 + -1.090909091 = -1.090909091 x = -1.090909091 Simplifying x = -1.090909091Subproblem 2
x + 1.090909091 = 0.000000000 Simplifying x + 1.090909091 = 0.000000000 Reorder the terms: 1.090909091 + x = 0.000000000 Solving 1.090909091 + x = 0.000000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.090909091' to each side of the equation. 1.090909091 + -1.090909091 + x = 0.000000000 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + x = 0.000000000 + -1.090909091 x = 0.000000000 + -1.090909091 Combine like terms: 0.000000000 + -1.090909091 = -1.090909091 x = -1.090909091 Simplifying x = -1.090909091Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.090909091, -1.090909091}
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