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Simplifying 6.3x2 + 42.7x + -425.1 = 0 Reorder the terms: -425.1 + 42.7x + 6.3x2 = 0 Solving -425.1 + 42.7x + 6.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.3 the coefficient of the squared term: Divide each side by '6.3'. -67.47619048 + 6.777777778x + x2 = 0 Move the constant term to the right: Add '67.47619048' to each side of the equation. -67.47619048 + 6.777777778x + 67.47619048 + x2 = 0 + 67.47619048 Reorder the terms: -67.47619048 + 67.47619048 + 6.777777778x + x2 = 0 + 67.47619048 Combine like terms: -67.47619048 + 67.47619048 = 0.00000000 0.00000000 + 6.777777778x + x2 = 0 + 67.47619048 6.777777778x + x2 = 0 + 67.47619048 Combine like terms: 0 + 67.47619048 = 67.47619048 6.777777778x + x2 = 67.47619048 The x term is 6.777777778x. Take half its coefficient (3.388888889). Square it (11.48456790) and add it to both sides. Add '11.48456790' to each side of the equation. 6.777777778x + 11.48456790 + x2 = 67.47619048 + 11.48456790 Reorder the terms: 11.48456790 + 6.777777778x + x2 = 67.47619048 + 11.48456790 Combine like terms: 67.47619048 + 11.48456790 = 78.96075838 11.48456790 + 6.777777778x + x2 = 78.96075838 Factor a perfect square on the left side: (x + 3.388888889)(x + 3.388888889) = 78.96075838 Calculate the square root of the right side: 8.88598663 Break this problem into two subproblems by setting (x + 3.388888889) equal to 8.88598663 and -8.88598663.Subproblem 1
x + 3.388888889 = 8.88598663 Simplifying x + 3.388888889 = 8.88598663 Reorder the terms: 3.388888889 + x = 8.88598663 Solving 3.388888889 + x = 8.88598663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.388888889' to each side of the equation. 3.388888889 + -3.388888889 + x = 8.88598663 + -3.388888889 Combine like terms: 3.388888889 + -3.388888889 = 0.000000000 0.000000000 + x = 8.88598663 + -3.388888889 x = 8.88598663 + -3.388888889 Combine like terms: 8.88598663 + -3.388888889 = 5.497097741 x = 5.497097741 Simplifying x = 5.497097741Subproblem 2
x + 3.388888889 = -8.88598663 Simplifying x + 3.388888889 = -8.88598663 Reorder the terms: 3.388888889 + x = -8.88598663 Solving 3.388888889 + x = -8.88598663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.388888889' to each side of the equation. 3.388888889 + -3.388888889 + x = -8.88598663 + -3.388888889 Combine like terms: 3.388888889 + -3.388888889 = 0.000000000 0.000000000 + x = -8.88598663 + -3.388888889 x = -8.88598663 + -3.388888889 Combine like terms: -8.88598663 + -3.388888889 = -12.274875519 x = -12.274875519 Simplifying x = -12.274875519Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.497097741, -12.274875519}
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