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Simplifying 20.22x2 + 3900x + 326 = 6.74 Reorder the terms: 326 + 3900x + 20.22x2 = 6.74 Solving 326 + 3900x + 20.22x2 = 6.74 Solving for variable 'x'. Reorder the terms: 326 + -6.74 + 3900x + 20.22x2 = 6.74 + -6.74 Combine like terms: 326 + -6.74 = 319.26 319.26 + 3900x + 20.22x2 = 6.74 + -6.74 Combine like terms: 6.74 + -6.74 = 0.00 319.26 + 3900x + 20.22x2 = 0.00 Begin completing the square. Divide all terms by 20.22 the coefficient of the squared term: Divide each side by '20.22'. 15.78931751 + 192.8783383x + x2 = 0 Move the constant term to the right: Add '-15.78931751' to each side of the equation. 15.78931751 + 192.8783383x + -15.78931751 + x2 = 0 + -15.78931751 Reorder the terms: 15.78931751 + -15.78931751 + 192.8783383x + x2 = 0 + -15.78931751 Combine like terms: 15.78931751 + -15.78931751 = 0.00000000 0.00000000 + 192.8783383x + x2 = 0 + -15.78931751 192.8783383x + x2 = 0 + -15.78931751 Combine like terms: 0 + -15.78931751 = -15.78931751 192.8783383x + x2 = -15.78931751 The x term is 192.8783383x. Take half its coefficient (96.43916915). Square it (9300.513346) and add it to both sides. Add '9300.513346' to each side of the equation. 192.8783383x + 9300.513346 + x2 = -15.78931751 + 9300.513346 Reorder the terms: 9300.513346 + 192.8783383x + x2 = -15.78931751 + 9300.513346 Combine like terms: -15.78931751 + 9300.513346 = 9284.72402849 9300.513346 + 192.8783383x + x2 = 9284.72402849 Factor a perfect square on the left side: (x + 96.43916915)(x + 96.43916915) = 9284.72402849 Calculate the square root of the right side: 96.357272837 Break this problem into two subproblems by setting (x + 96.43916915) equal to 96.357272837 and -96.357272837.Subproblem 1
x + 96.43916915 = 96.357272837 Simplifying x + 96.43916915 = 96.357272837 Reorder the terms: 96.43916915 + x = 96.357272837 Solving 96.43916915 + x = 96.357272837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-96.43916915' to each side of the equation. 96.43916915 + -96.43916915 + x = 96.357272837 + -96.43916915 Combine like terms: 96.43916915 + -96.43916915 = 0.00000000 0.00000000 + x = 96.357272837 + -96.43916915 x = 96.357272837 + -96.43916915 Combine like terms: 96.357272837 + -96.43916915 = -0.081896313 x = -0.081896313 Simplifying x = -0.081896313Subproblem 2
x + 96.43916915 = -96.357272837 Simplifying x + 96.43916915 = -96.357272837 Reorder the terms: 96.43916915 + x = -96.357272837 Solving 96.43916915 + x = -96.357272837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-96.43916915' to each side of the equation. 96.43916915 + -96.43916915 + x = -96.357272837 + -96.43916915 Combine like terms: 96.43916915 + -96.43916915 = 0.00000000 0.00000000 + x = -96.357272837 + -96.43916915 x = -96.357272837 + -96.43916915 Combine like terms: -96.357272837 + -96.43916915 = -192.796441987 x = -192.796441987 Simplifying x = -192.796441987Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.081896313, -192.796441987}
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