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Simplifying 36x2 + 28x + -13 = 0 Reorder the terms: -13 + 28x + 36x2 = 0 Solving -13 + 28x + 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'. -0.3611111111 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.7777777778x + 0.3611111111 + x2 = 0 + 0.3611111111 Reorder the terms: -0.3611111111 + 0.3611111111 + 0.7777777778x + x2 = 0 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + 0.3611111111 0.7777777778x + x2 = 0 + 0.3611111111 Combine like terms: 0 + 0.3611111111 = 0.3611111111 0.7777777778x + x2 = 0.3611111111 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 0.3611111111 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 0.3611111111 + 0.1512345679 Combine like terms: 0.3611111111 + 0.1512345679 = 0.512345679 0.1512345679 + 0.7777777778x + x2 = 0.512345679 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 0.512345679 Calculate the square root of the right side: 0.715783263 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 0.715783263 and -0.715783263.Subproblem 1
x + 0.3888888889 = 0.715783263 Simplifying x + 0.3888888889 = 0.715783263 Reorder the terms: 0.3888888889 + x = 0.715783263 Solving 0.3888888889 + x = 0.715783263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 0.715783263 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 0.715783263 + -0.3888888889 x = 0.715783263 + -0.3888888889 Combine like terms: 0.715783263 + -0.3888888889 = 0.3268943741 x = 0.3268943741 Simplifying x = 0.3268943741Subproblem 2
x + 0.3888888889 = -0.715783263 Simplifying x + 0.3888888889 = -0.715783263 Reorder the terms: 0.3888888889 + x = -0.715783263 Solving 0.3888888889 + x = -0.715783263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -0.715783263 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -0.715783263 + -0.3888888889 x = -0.715783263 + -0.3888888889 Combine like terms: -0.715783263 + -0.3888888889 = -1.1046721519 x = -1.1046721519 Simplifying x = -1.1046721519Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3268943741, -1.1046721519}
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