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Simplifying 9x2 + 52x + -7 = 0 Reorder the terms: -7 + 52x + 9x2 = 0 Solving -7 + 52x + 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'. -0.7777777778 + 5.777777778x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 5.777777778x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 5.777777778x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 5.777777778x + x2 = 0 + 0.7777777778 5.777777778x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 5.777777778x + x2 = 0.7777777778 The x term is 5.777777778x. Take half its coefficient (2.888888889). Square it (8.345679013) and add it to both sides. Add '8.345679013' to each side of the equation. 5.777777778x + 8.345679013 + x2 = 0.7777777778 + 8.345679013 Reorder the terms: 8.345679013 + 5.777777778x + x2 = 0.7777777778 + 8.345679013 Combine like terms: 0.7777777778 + 8.345679013 = 9.1234567908 8.345679013 + 5.777777778x + x2 = 9.1234567908 Factor a perfect square on the left side: (x + 2.888888889)(x + 2.888888889) = 9.1234567908 Calculate the square root of the right side: 3.020506049 Break this problem into two subproblems by setting (x + 2.888888889) equal to 3.020506049 and -3.020506049.Subproblem 1
x + 2.888888889 = 3.020506049 Simplifying x + 2.888888889 = 3.020506049 Reorder the terms: 2.888888889 + x = 3.020506049 Solving 2.888888889 + x = 3.020506049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.888888889' to each side of the equation. 2.888888889 + -2.888888889 + x = 3.020506049 + -2.888888889 Combine like terms: 2.888888889 + -2.888888889 = 0.000000000 0.000000000 + x = 3.020506049 + -2.888888889 x = 3.020506049 + -2.888888889 Combine like terms: 3.020506049 + -2.888888889 = 0.13161716 x = 0.13161716 Simplifying x = 0.13161716Subproblem 2
x + 2.888888889 = -3.020506049 Simplifying x + 2.888888889 = -3.020506049 Reorder the terms: 2.888888889 + x = -3.020506049 Solving 2.888888889 + x = -3.020506049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.888888889' to each side of the equation. 2.888888889 + -2.888888889 + x = -3.020506049 + -2.888888889 Combine like terms: 2.888888889 + -2.888888889 = 0.000000000 0.000000000 + x = -3.020506049 + -2.888888889 x = -3.020506049 + -2.888888889 Combine like terms: -3.020506049 + -2.888888889 = -5.909394938 x = -5.909394938 Simplifying x = -5.909394938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13161716, -5.909394938}
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