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Simplifying 72x2 + -29x + 1 = 0 Reorder the terms: 1 + -29x + 72x2 = 0 Solving 1 + -29x + 72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 0.01388888889 + -0.4027777778x + x2 = 0 Move the constant term to the right: Add '-0.01388888889' to each side of the equation. 0.01388888889 + -0.4027777778x + -0.01388888889 + x2 = 0 + -0.01388888889 Reorder the terms: 0.01388888889 + -0.01388888889 + -0.4027777778x + x2 = 0 + -0.01388888889 Combine like terms: 0.01388888889 + -0.01388888889 = 0.00000000000 0.00000000000 + -0.4027777778x + x2 = 0 + -0.01388888889 -0.4027777778x + x2 = 0 + -0.01388888889 Combine like terms: 0 + -0.01388888889 = -0.01388888889 -0.4027777778x + x2 = -0.01388888889 The x term is -0.4027777778x. Take half its coefficient (-0.2013888889). Square it (0.04055748457) and add it to both sides. Add '0.04055748457' to each side of the equation. -0.4027777778x + 0.04055748457 + x2 = -0.01388888889 + 0.04055748457 Reorder the terms: 0.04055748457 + -0.4027777778x + x2 = -0.01388888889 + 0.04055748457 Combine like terms: -0.01388888889 + 0.04055748457 = 0.02666859568 0.04055748457 + -0.4027777778x + x2 = 0.02666859568 Factor a perfect square on the left side: (x + -0.2013888889)(x + -0.2013888889) = 0.02666859568 Calculate the square root of the right side: 0.163305222 Break this problem into two subproblems by setting (x + -0.2013888889) equal to 0.163305222 and -0.163305222.Subproblem 1
x + -0.2013888889 = 0.163305222 Simplifying x + -0.2013888889 = 0.163305222 Reorder the terms: -0.2013888889 + x = 0.163305222 Solving -0.2013888889 + x = 0.163305222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2013888889' to each side of the equation. -0.2013888889 + 0.2013888889 + x = 0.163305222 + 0.2013888889 Combine like terms: -0.2013888889 + 0.2013888889 = 0.0000000000 0.0000000000 + x = 0.163305222 + 0.2013888889 x = 0.163305222 + 0.2013888889 Combine like terms: 0.163305222 + 0.2013888889 = 0.3646941109 x = 0.3646941109 Simplifying x = 0.3646941109Subproblem 2
x + -0.2013888889 = -0.163305222 Simplifying x + -0.2013888889 = -0.163305222 Reorder the terms: -0.2013888889 + x = -0.163305222 Solving -0.2013888889 + x = -0.163305222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2013888889' to each side of the equation. -0.2013888889 + 0.2013888889 + x = -0.163305222 + 0.2013888889 Combine like terms: -0.2013888889 + 0.2013888889 = 0.0000000000 0.0000000000 + x = -0.163305222 + 0.2013888889 x = -0.163305222 + 0.2013888889 Combine like terms: -0.163305222 + 0.2013888889 = 0.0380836669 x = 0.0380836669 Simplifying x = 0.0380836669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3646941109, 0.0380836669}
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