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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 = 9316.30266351 9300.513346 + -192.8783383x + x2 = 9316.30266351 Factor a perfect square on the left side: (x + -96.43916915)(x + -96.43916915) = 9316.30266351 Calculate the square root of the right side: 96.520995972 Break this problem into two subproblems by setting (x + -96.43916915) equal to 96.520995972 and -96.520995972.Subproblem 1
x + -96.43916915 = 96.520995972 Simplifying x + -96.43916915 = 96.520995972 Reorder the terms: -96.43916915 + x = 96.520995972 Solving -96.43916915 + x = 96.520995972 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 = 96.520995972 + 96.43916915 Combine like terms: -96.43916915 + 96.43916915 = 0.00000000 0.00000000 + x = 96.520995972 + 96.43916915 x = 96.520995972 + 96.43916915 Combine like terms: 96.520995972 + 96.43916915 = 192.960165122 x = 192.960165122 Simplifying x = 192.960165122Subproblem 2
x + -96.43916915 = -96.520995972 Simplifying x + -96.43916915 = -96.520995972 Reorder the terms: -96.43916915 + x = -96.520995972 Solving -96.43916915 + x = -96.520995972 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 = -96.520995972 + 96.43916915 Combine like terms: -96.43916915 + 96.43916915 = 0.00000000 0.00000000 + x = -96.520995972 + 96.43916915 x = -96.520995972 + 96.43916915 Combine like terms: -96.520995972 + 96.43916915 = -0.081826822 x = -0.081826822 Simplifying x = -0.081826822Solution
The solution to the problem is based on the solutions from the subproblems. x = {192.960165122, -0.081826822}
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