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Simplifying 9x2 + -7x + -10000 = 0 Reorder the terms: -10000 + -7x + 9x2 = 0 Solving -10000 + -7x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1111.111111 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '1111.111111' to each side of the equation. -1111.111111 + -0.7777777778x + 1111.111111 + x2 = 0 + 1111.111111 Reorder the terms: -1111.111111 + 1111.111111 + -0.7777777778x + x2 = 0 + 1111.111111 Combine like terms: -1111.111111 + 1111.111111 = 0.000000 0.000000 + -0.7777777778x + x2 = 0 + 1111.111111 -0.7777777778x + x2 = 0 + 1111.111111 Combine like terms: 0 + 1111.111111 = 1111.111111 -0.7777777778x + x2 = 1111.111111 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 = 1111.111111 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 1111.111111 + 0.1512345679 Combine like terms: 1111.111111 + 0.1512345679 = 1111.2623455679 0.1512345679 + -0.7777777778x + x2 = 1111.2623455679 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 1111.2623455679 Calculate the square root of the right side: 33.335601773 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 33.335601773 and -33.335601773.Subproblem 1
x + -0.3888888889 = 33.335601773 Simplifying x + -0.3888888889 = 33.335601773 Reorder the terms: -0.3888888889 + x = 33.335601773 Solving -0.3888888889 + x = 33.335601773 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 = 33.335601773 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 33.335601773 + 0.3888888889 x = 33.335601773 + 0.3888888889 Combine like terms: 33.335601773 + 0.3888888889 = 33.7244906619 x = 33.7244906619 Simplifying x = 33.7244906619Subproblem 2
x + -0.3888888889 = -33.335601773 Simplifying x + -0.3888888889 = -33.335601773 Reorder the terms: -0.3888888889 + x = -33.335601773 Solving -0.3888888889 + x = -33.335601773 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 = -33.335601773 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -33.335601773 + 0.3888888889 x = -33.335601773 + 0.3888888889 Combine like terms: -33.335601773 + 0.3888888889 = -32.9467128841 x = -32.9467128841 Simplifying x = -32.9467128841Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.7244906619, -32.9467128841}
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