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Simplifying 22x2 + -69x + 26 = 0 Reorder the terms: 26 + -69x + 22x2 = 0 Solving 26 + -69x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. 1.181818182 + -3.136363636x + x2 = 0 Move the constant term to the right: Add '-1.181818182' to each side of the equation. 1.181818182 + -3.136363636x + -1.181818182 + x2 = 0 + -1.181818182 Reorder the terms: 1.181818182 + -1.181818182 + -3.136363636x + x2 = 0 + -1.181818182 Combine like terms: 1.181818182 + -1.181818182 = 0.000000000 0.000000000 + -3.136363636x + x2 = 0 + -1.181818182 -3.136363636x + x2 = 0 + -1.181818182 Combine like terms: 0 + -1.181818182 = -1.181818182 -3.136363636x + x2 = -1.181818182 The x term is -3.136363636x. Take half its coefficient (-1.568181818). Square it (2.459194214) and add it to both sides. Add '2.459194214' to each side of the equation. -3.136363636x + 2.459194214 + x2 = -1.181818182 + 2.459194214 Reorder the terms: 2.459194214 + -3.136363636x + x2 = -1.181818182 + 2.459194214 Combine like terms: -1.181818182 + 2.459194214 = 1.277376032 2.459194214 + -3.136363636x + x2 = 1.277376032 Factor a perfect square on the left side: (x + -1.568181818)(x + -1.568181818) = 1.277376032 Calculate the square root of the right side: 1.130210614 Break this problem into two subproblems by setting (x + -1.568181818) equal to 1.130210614 and -1.130210614.Subproblem 1
x + -1.568181818 = 1.130210614 Simplifying x + -1.568181818 = 1.130210614 Reorder the terms: -1.568181818 + x = 1.130210614 Solving -1.568181818 + x = 1.130210614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.568181818' to each side of the equation. -1.568181818 + 1.568181818 + x = 1.130210614 + 1.568181818 Combine like terms: -1.568181818 + 1.568181818 = 0.000000000 0.000000000 + x = 1.130210614 + 1.568181818 x = 1.130210614 + 1.568181818 Combine like terms: 1.130210614 + 1.568181818 = 2.698392432 x = 2.698392432 Simplifying x = 2.698392432Subproblem 2
x + -1.568181818 = -1.130210614 Simplifying x + -1.568181818 = -1.130210614 Reorder the terms: -1.568181818 + x = -1.130210614 Solving -1.568181818 + x = -1.130210614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.568181818' to each side of the equation. -1.568181818 + 1.568181818 + x = -1.130210614 + 1.568181818 Combine like terms: -1.568181818 + 1.568181818 = 0.000000000 0.000000000 + x = -1.130210614 + 1.568181818 x = -1.130210614 + 1.568181818 Combine like terms: -1.130210614 + 1.568181818 = 0.437971204 x = 0.437971204 Simplifying x = 0.437971204Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.698392432, 0.437971204}
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