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Simplifying 3.405X2 + -10.6168X + 4.8837 = 0 Reorder the terms: 4.8837 + -10.6168X + 3.405X2 = 0 Solving 4.8837 + -10.6168X + 3.405X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3.405 the coefficient of the squared term: Divide each side by '3.405'. 1.434273128 + -3.118002937X + X2 = 0 Move the constant term to the right: Add '-1.434273128' to each side of the equation. 1.434273128 + -3.118002937X + -1.434273128 + X2 = 0 + -1.434273128 Reorder the terms: 1.434273128 + -1.434273128 + -3.118002937X + X2 = 0 + -1.434273128 Combine like terms: 1.434273128 + -1.434273128 = 0.000000000 0.000000000 + -3.118002937X + X2 = 0 + -1.434273128 -3.118002937X + X2 = 0 + -1.434273128 Combine like terms: 0 + -1.434273128 = -1.434273128 -3.118002937X + X2 = -1.434273128 The X term is -3.118002937X. Take half its coefficient (-1.559001469). Square it (2.430485580) and add it to both sides. Add '2.430485580' to each side of the equation. -3.118002937X + 2.430485580 + X2 = -1.434273128 + 2.430485580 Reorder the terms: 2.430485580 + -3.118002937X + X2 = -1.434273128 + 2.430485580 Combine like terms: -1.434273128 + 2.430485580 = 0.996212452 2.430485580 + -3.118002937X + X2 = 0.996212452 Factor a perfect square on the left side: (X + -1.559001469)(X + -1.559001469) = 0.996212452 Calculate the square root of the right side: 0.998104429 Break this problem into two subproblems by setting (X + -1.559001469) equal to 0.998104429 and -0.998104429.Subproblem 1
X + -1.559001469 = 0.998104429 Simplifying X + -1.559001469 = 0.998104429 Reorder the terms: -1.559001469 + X = 0.998104429 Solving -1.559001469 + X = 0.998104429 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.559001469' to each side of the equation. -1.559001469 + 1.559001469 + X = 0.998104429 + 1.559001469 Combine like terms: -1.559001469 + 1.559001469 = 0.000000000 0.000000000 + X = 0.998104429 + 1.559001469 X = 0.998104429 + 1.559001469 Combine like terms: 0.998104429 + 1.559001469 = 2.557105898 X = 2.557105898 Simplifying X = 2.557105898Subproblem 2
X + -1.559001469 = -0.998104429 Simplifying X + -1.559001469 = -0.998104429 Reorder the terms: -1.559001469 + X = -0.998104429 Solving -1.559001469 + X = -0.998104429 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.559001469' to each side of the equation. -1.559001469 + 1.559001469 + X = -0.998104429 + 1.559001469 Combine like terms: -1.559001469 + 1.559001469 = 0.000000000 0.000000000 + X = -0.998104429 + 1.559001469 X = -0.998104429 + 1.559001469 Combine like terms: -0.998104429 + 1.559001469 = 0.56089704 X = 0.56089704 Simplifying X = 0.56089704Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.557105898, 0.56089704}
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