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Simplifying 9x2 + 61x + 14 = 0 Reorder the terms: 14 + 61x + 9x2 = 0 Solving 14 + 61x + 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'. 1.555555556 + 6.777777778x + x2 = 0 Move the constant term to the right: Add '-1.555555556' to each side of the equation. 1.555555556 + 6.777777778x + -1.555555556 + x2 = 0 + -1.555555556 Reorder the terms: 1.555555556 + -1.555555556 + 6.777777778x + x2 = 0 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + 6.777777778x + x2 = 0 + -1.555555556 6.777777778x + x2 = 0 + -1.555555556 Combine like terms: 0 + -1.555555556 = -1.555555556 6.777777778x + x2 = -1.555555556 The x term is 6.777777778x. Take half its coefficient (3.388888889). Square it (11.48456790) and add it to both sides. Add '11.48456790' to each side of the equation. 6.777777778x + 11.48456790 + x2 = -1.555555556 + 11.48456790 Reorder the terms: 11.48456790 + 6.777777778x + x2 = -1.555555556 + 11.48456790 Combine like terms: -1.555555556 + 11.48456790 = 9.929012344 11.48456790 + 6.777777778x + x2 = 9.929012344 Factor a perfect square on the left side: (x + 3.388888889)(x + 3.388888889) = 9.929012344 Calculate the square root of the right side: 3.151033536 Break this problem into two subproblems by setting (x + 3.388888889) equal to 3.151033536 and -3.151033536.Subproblem 1
x + 3.388888889 = 3.151033536 Simplifying x + 3.388888889 = 3.151033536 Reorder the terms: 3.388888889 + x = 3.151033536 Solving 3.388888889 + x = 3.151033536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.388888889' to each side of the equation. 3.388888889 + -3.388888889 + x = 3.151033536 + -3.388888889 Combine like terms: 3.388888889 + -3.388888889 = 0.000000000 0.000000000 + x = 3.151033536 + -3.388888889 x = 3.151033536 + -3.388888889 Combine like terms: 3.151033536 + -3.388888889 = -0.237855353 x = -0.237855353 Simplifying x = -0.237855353Subproblem 2
x + 3.388888889 = -3.151033536 Simplifying x + 3.388888889 = -3.151033536 Reorder the terms: 3.388888889 + x = -3.151033536 Solving 3.388888889 + x = -3.151033536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.388888889' to each side of the equation. 3.388888889 + -3.388888889 + x = -3.151033536 + -3.388888889 Combine like terms: 3.388888889 + -3.388888889 = 0.000000000 0.000000000 + x = -3.151033536 + -3.388888889 x = -3.151033536 + -3.388888889 Combine like terms: -3.151033536 + -3.388888889 = -6.539922425 x = -6.539922425 Simplifying x = -6.539922425Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.237855353, -6.539922425}
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