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Simplifying 36x2 + 64x + 25 = 0 Reorder the terms: 25 + 64x + 36x2 = 0 Solving 25 + 64x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.6944444444 + 1.777777778x + x2 = 0 Move the constant term to the right: Add '-0.6944444444' to each side of the equation. 0.6944444444 + 1.777777778x + -0.6944444444 + x2 = 0 + -0.6944444444 Reorder the terms: 0.6944444444 + -0.6944444444 + 1.777777778x + x2 = 0 + -0.6944444444 Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000 0.0000000000 + 1.777777778x + x2 = 0 + -0.6944444444 1.777777778x + x2 = 0 + -0.6944444444 Combine like terms: 0 + -0.6944444444 = -0.6944444444 1.777777778x + x2 = -0.6944444444 The x term is 1.777777778x. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778x + 0.7901234570 + x2 = -0.6944444444 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778x + x2 = -0.6944444444 + 0.7901234570 Combine like terms: -0.6944444444 + 0.7901234570 = 0.0956790126 0.7901234570 + 1.777777778x + x2 = 0.0956790126 Factor a perfect square on the left side: (x + 0.888888889)(x + 0.888888889) = 0.0956790126 Calculate the square root of the right side: 0.309320243 Break this problem into two subproblems by setting (x + 0.888888889) equal to 0.309320243 and -0.309320243.Subproblem 1
x + 0.888888889 = 0.309320243 Simplifying x + 0.888888889 = 0.309320243 Reorder the terms: 0.888888889 + x = 0.309320243 Solving 0.888888889 + x = 0.309320243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = 0.309320243 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = 0.309320243 + -0.888888889 x = 0.309320243 + -0.888888889 Combine like terms: 0.309320243 + -0.888888889 = -0.579568646 x = -0.579568646 Simplifying x = -0.579568646Subproblem 2
x + 0.888888889 = -0.309320243 Simplifying x + 0.888888889 = -0.309320243 Reorder the terms: 0.888888889 + x = -0.309320243 Solving 0.888888889 + x = -0.309320243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + x = -0.309320243 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + x = -0.309320243 + -0.888888889 x = -0.309320243 + -0.888888889 Combine like terms: -0.309320243 + -0.888888889 = -1.198209132 x = -1.198209132 Simplifying x = -1.198209132Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.579568646, -1.198209132}
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