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Simplifying 9x2 + 103x + 269 = 0 Reorder the terms: 269 + 103x + 9x2 = 0 Solving 269 + 103x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 29.88888889 + 11.44444444x + x2 = 0 Move the constant term to the right: Add '-29.88888889' to each side of the equation. 29.88888889 + 11.44444444x + -29.88888889 + x2 = 0 + -29.88888889 Reorder the terms: 29.88888889 + -29.88888889 + 11.44444444x + x2 = 0 + -29.88888889 Combine like terms: 29.88888889 + -29.88888889 = 0.00000000 0.00000000 + 11.44444444x + x2 = 0 + -29.88888889 11.44444444x + x2 = 0 + -29.88888889 Combine like terms: 0 + -29.88888889 = -29.88888889 11.44444444x + x2 = -29.88888889 The x term is 11.44444444x. Take half its coefficient (5.72222222). Square it (32.74382714) and add it to both sides. Add '32.74382714' to each side of the equation. 11.44444444x + 32.74382714 + x2 = -29.88888889 + 32.74382714 Reorder the terms: 32.74382714 + 11.44444444x + x2 = -29.88888889 + 32.74382714 Combine like terms: -29.88888889 + 32.74382714 = 2.85493825 32.74382714 + 11.44444444x + x2 = 2.85493825 Factor a perfect square on the left side: (x + 5.72222222)(x + 5.72222222) = 2.85493825 Calculate the square root of the right side: 1.689656252 Break this problem into two subproblems by setting (x + 5.72222222) equal to 1.689656252 and -1.689656252.Subproblem 1
x + 5.72222222 = 1.689656252 Simplifying x + 5.72222222 = 1.689656252 Reorder the terms: 5.72222222 + x = 1.689656252 Solving 5.72222222 + x = 1.689656252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.72222222' to each side of the equation. 5.72222222 + -5.72222222 + x = 1.689656252 + -5.72222222 Combine like terms: 5.72222222 + -5.72222222 = 0.00000000 0.00000000 + x = 1.689656252 + -5.72222222 x = 1.689656252 + -5.72222222 Combine like terms: 1.689656252 + -5.72222222 = -4.032565968 x = -4.032565968 Simplifying x = -4.032565968Subproblem 2
x + 5.72222222 = -1.689656252 Simplifying x + 5.72222222 = -1.689656252 Reorder the terms: 5.72222222 + x = -1.689656252 Solving 5.72222222 + x = -1.689656252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.72222222' to each side of the equation. 5.72222222 + -5.72222222 + x = -1.689656252 + -5.72222222 Combine like terms: 5.72222222 + -5.72222222 = 0.00000000 0.00000000 + x = -1.689656252 + -5.72222222 x = -1.689656252 + -5.72222222 Combine like terms: -1.689656252 + -5.72222222 = -7.411878472 x = -7.411878472 Simplifying x = -7.411878472Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.032565968, -7.411878472}
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