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Simplifying 9x2 + 0.7x = 0.05 Reorder the terms: 0.7x + 9x2 = 0.05 Solving 0.7x + 9x2 = 0.05 Solving for variable 'x'. Reorder the terms: -0.05 + 0.7x + 9x2 = 0.05 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 -0.05 + 0.7x + 9x2 = 0.00 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.005555555556 + 0.07777777778x + x2 = 0.00 Move the constant term to the right: Add '0.005555555556' to each side of the equation. -0.005555555556 + 0.07777777778x + 0.005555555556 + x2 = 0.00 + 0.005555555556 Reorder the terms: -0.005555555556 + 0.005555555556 + 0.07777777778x + x2 = 0.00 + 0.005555555556 Combine like terms: -0.005555555556 + 0.005555555556 = 0.000000000000 0.000000000000 + 0.07777777778x + x2 = 0.00 + 0.005555555556 0.07777777778x + x2 = 0.00 + 0.005555555556 Combine like terms: 0.00 + 0.005555555556 = 0.005555555556 0.07777777778x + x2 = 0.005555555556 The x term is 0.07777777778x. Take half its coefficient (0.03888888889). Square it (0.001512345679) and add it to both sides. Add '0.001512345679' to each side of the equation. 0.07777777778x + 0.001512345679 + x2 = 0.005555555556 + 0.001512345679 Reorder the terms: 0.001512345679 + 0.07777777778x + x2 = 0.005555555556 + 0.001512345679 Combine like terms: 0.005555555556 + 0.001512345679 = 0.007067901235 0.001512345679 + 0.07777777778x + x2 = 0.007067901235 Factor a perfect square on the left side: (x + 0.03888888889)(x + 0.03888888889) = 0.007067901235 Calculate the square root of the right side: 0.084070811 Break this problem into two subproblems by setting (x + 0.03888888889) equal to 0.084070811 and -0.084070811.Subproblem 1
x + 0.03888888889 = 0.084070811 Simplifying x + 0.03888888889 = 0.084070811 Reorder the terms: 0.03888888889 + x = 0.084070811 Solving 0.03888888889 + x = 0.084070811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03888888889' to each side of the equation. 0.03888888889 + -0.03888888889 + x = 0.084070811 + -0.03888888889 Combine like terms: 0.03888888889 + -0.03888888889 = 0.00000000000 0.00000000000 + x = 0.084070811 + -0.03888888889 x = 0.084070811 + -0.03888888889 Combine like terms: 0.084070811 + -0.03888888889 = 0.04518192211 x = 0.04518192211 Simplifying x = 0.04518192211Subproblem 2
x + 0.03888888889 = -0.084070811 Simplifying x + 0.03888888889 = -0.084070811 Reorder the terms: 0.03888888889 + x = -0.084070811 Solving 0.03888888889 + x = -0.084070811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03888888889' to each side of the equation. 0.03888888889 + -0.03888888889 + x = -0.084070811 + -0.03888888889 Combine like terms: 0.03888888889 + -0.03888888889 = 0.00000000000 0.00000000000 + x = -0.084070811 + -0.03888888889 x = -0.084070811 + -0.03888888889 Combine like terms: -0.084070811 + -0.03888888889 = -0.12295969989 x = -0.12295969989 Simplifying x = -0.12295969989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.04518192211, -0.12295969989}
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