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Simplifying 20.6x2 + -73.4x + 41.8 = 0 Reorder the terms: 41.8 + -73.4x + 20.6x2 = 0 Solving 41.8 + -73.4x + 20.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20.6 the coefficient of the squared term: Divide each side by '20.6'. 2.029126214 + -3.563106796x + x2 = 0 Move the constant term to the right: Add '-2.029126214' to each side of the equation. 2.029126214 + -3.563106796x + -2.029126214 + x2 = 0 + -2.029126214 Reorder the terms: 2.029126214 + -2.029126214 + -3.563106796x + x2 = 0 + -2.029126214 Combine like terms: 2.029126214 + -2.029126214 = 0.000000000 0.000000000 + -3.563106796x + x2 = 0 + -2.029126214 -3.563106796x + x2 = 0 + -2.029126214 Combine like terms: 0 + -2.029126214 = -2.029126214 -3.563106796x + x2 = -2.029126214 The x term is -3.563106796x. Take half its coefficient (-1.781553398). Square it (3.173932510) and add it to both sides. Add '3.173932510' to each side of the equation. -3.563106796x + 3.173932510 + x2 = -2.029126214 + 3.173932510 Reorder the terms: 3.173932510 + -3.563106796x + x2 = -2.029126214 + 3.173932510 Combine like terms: -2.029126214 + 3.173932510 = 1.144806296 3.173932510 + -3.563106796x + x2 = 1.144806296 Factor a perfect square on the left side: (x + -1.781553398)(x + -1.781553398) = 1.144806296 Calculate the square root of the right side: 1.069956212 Break this problem into two subproblems by setting (x + -1.781553398) equal to 1.069956212 and -1.069956212.Subproblem 1
x + -1.781553398 = 1.069956212 Simplifying x + -1.781553398 = 1.069956212 Reorder the terms: -1.781553398 + x = 1.069956212 Solving -1.781553398 + x = 1.069956212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.781553398' to each side of the equation. -1.781553398 + 1.781553398 + x = 1.069956212 + 1.781553398 Combine like terms: -1.781553398 + 1.781553398 = 0.000000000 0.000000000 + x = 1.069956212 + 1.781553398 x = 1.069956212 + 1.781553398 Combine like terms: 1.069956212 + 1.781553398 = 2.85150961 x = 2.85150961 Simplifying x = 2.85150961Subproblem 2
x + -1.781553398 = -1.069956212 Simplifying x + -1.781553398 = -1.069956212 Reorder the terms: -1.781553398 + x = -1.069956212 Solving -1.781553398 + x = -1.069956212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.781553398' to each side of the equation. -1.781553398 + 1.781553398 + x = -1.069956212 + 1.781553398 Combine like terms: -1.781553398 + 1.781553398 = 0.000000000 0.000000000 + x = -1.069956212 + 1.781553398 x = -1.069956212 + 1.781553398 Combine like terms: -1.069956212 + 1.781553398 = 0.711597186 x = 0.711597186 Simplifying x = 0.711597186Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.85150961, 0.711597186}
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