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Simplifying 16.1x2 + -20x + 4 = 0 Reorder the terms: 4 + -20x + 16.1x2 = 0 Solving 4 + -20x + 16.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16.1 the coefficient of the squared term: Divide each side by '16.1'. 0.248447205 + -1.242236025x + x2 = 0 Move the constant term to the right: Add '-0.248447205' to each side of the equation. 0.248447205 + -1.242236025x + -0.248447205 + x2 = 0 + -0.248447205 Reorder the terms: 0.248447205 + -0.248447205 + -1.242236025x + x2 = 0 + -0.248447205 Combine like terms: 0.248447205 + -0.248447205 = 0.000000000 0.000000000 + -1.242236025x + x2 = 0 + -0.248447205 -1.242236025x + x2 = 0 + -0.248447205 Combine like terms: 0 + -0.248447205 = -0.248447205 -1.242236025x + x2 = -0.248447205 The x term is -1.242236025x. Take half its coefficient (-0.6211180125). Square it (0.3857875855) and add it to both sides. Add '0.3857875855' to each side of the equation. -1.242236025x + 0.3857875855 + x2 = -0.248447205 + 0.3857875855 Reorder the terms: 0.3857875855 + -1.242236025x + x2 = -0.248447205 + 0.3857875855 Combine like terms: -0.248447205 + 0.3857875855 = 0.1373403805 0.3857875855 + -1.242236025x + x2 = 0.1373403805 Factor a perfect square on the left side: (x + -0.6211180125)(x + -0.6211180125) = 0.1373403805 Calculate the square root of the right side: 0.370594631 Break this problem into two subproblems by setting (x + -0.6211180125) equal to 0.370594631 and -0.370594631.Subproblem 1
x + -0.6211180125 = 0.370594631 Simplifying x + -0.6211180125 = 0.370594631 Reorder the terms: -0.6211180125 + x = 0.370594631 Solving -0.6211180125 + x = 0.370594631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6211180125' to each side of the equation. -0.6211180125 + 0.6211180125 + x = 0.370594631 + 0.6211180125 Combine like terms: -0.6211180125 + 0.6211180125 = 0.0000000000 0.0000000000 + x = 0.370594631 + 0.6211180125 x = 0.370594631 + 0.6211180125 Combine like terms: 0.370594631 + 0.6211180125 = 0.9917126435 x = 0.9917126435 Simplifying x = 0.9917126435Subproblem 2
x + -0.6211180125 = -0.370594631 Simplifying x + -0.6211180125 = -0.370594631 Reorder the terms: -0.6211180125 + x = -0.370594631 Solving -0.6211180125 + x = -0.370594631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6211180125' to each side of the equation. -0.6211180125 + 0.6211180125 + x = -0.370594631 + 0.6211180125 Combine like terms: -0.6211180125 + 0.6211180125 = 0.0000000000 0.0000000000 + x = -0.370594631 + 0.6211180125 x = -0.370594631 + 0.6211180125 Combine like terms: -0.370594631 + 0.6211180125 = 0.2505233815 x = 0.2505233815 Simplifying x = 0.2505233815Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9917126435, 0.2505233815}
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