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Simplifying 0 = -9x2 + 295x + 1000 Reorder the terms: 0 = 1000 + 295x + -9x2 Solving 0 = 1000 + 295x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -1000 = -1000 -1000 + -295x + 9x2 = 1000 + 295x + -9x2 + -1000 + -295x + 9x2 Reorder the terms: -1000 + -295x + 9x2 = 1000 + -1000 + 295x + -295x + -9x2 + 9x2 Combine like terms: 1000 + -1000 = 0 -1000 + -295x + 9x2 = 0 + 295x + -295x + -9x2 + 9x2 -1000 + -295x + 9x2 = 295x + -295x + -9x2 + 9x2 Combine like terms: 295x + -295x = 0 -1000 + -295x + 9x2 = 0 + -9x2 + 9x2 -1000 + -295x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -1000 + -295x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -111.1111111 + -32.77777778x + x2 = 0 Move the constant term to the right: Add '111.1111111' to each side of the equation. -111.1111111 + -32.77777778x + 111.1111111 + x2 = 0 + 111.1111111 Reorder the terms: -111.1111111 + 111.1111111 + -32.77777778x + x2 = 0 + 111.1111111 Combine like terms: -111.1111111 + 111.1111111 = 0.0000000 0.0000000 + -32.77777778x + x2 = 0 + 111.1111111 -32.77777778x + x2 = 0 + 111.1111111 Combine like terms: 0 + 111.1111111 = 111.1111111 -32.77777778x + x2 = 111.1111111 The x term is -32.77777778x. Take half its coefficient (-16.38888889). Square it (268.5956790) and add it to both sides. Add '268.5956790' to each side of the equation. -32.77777778x + 268.5956790 + x2 = 111.1111111 + 268.5956790 Reorder the terms: 268.5956790 + -32.77777778x + x2 = 111.1111111 + 268.5956790 Combine like terms: 111.1111111 + 268.5956790 = 379.7067901 268.5956790 + -32.77777778x + x2 = 379.7067901 Factor a perfect square on the left side: (x + -16.38888889)(x + -16.38888889) = 379.7067901 Calculate the square root of the right side: 19.486066563 Break this problem into two subproblems by setting (x + -16.38888889) equal to 19.486066563 and -19.486066563.Subproblem 1
x + -16.38888889 = 19.486066563 Simplifying x + -16.38888889 = 19.486066563 Reorder the terms: -16.38888889 + x = 19.486066563 Solving -16.38888889 + x = 19.486066563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.38888889' to each side of the equation. -16.38888889 + 16.38888889 + x = 19.486066563 + 16.38888889 Combine like terms: -16.38888889 + 16.38888889 = 0.00000000 0.00000000 + x = 19.486066563 + 16.38888889 x = 19.486066563 + 16.38888889 Combine like terms: 19.486066563 + 16.38888889 = 35.874955453 x = 35.874955453 Simplifying x = 35.874955453Subproblem 2
x + -16.38888889 = -19.486066563 Simplifying x + -16.38888889 = -19.486066563 Reorder the terms: -16.38888889 + x = -19.486066563 Solving -16.38888889 + x = -19.486066563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.38888889' to each side of the equation. -16.38888889 + 16.38888889 + x = -19.486066563 + 16.38888889 Combine like terms: -16.38888889 + 16.38888889 = 0.00000000 0.00000000 + x = -19.486066563 + 16.38888889 x = -19.486066563 + 16.38888889 Combine like terms: -19.486066563 + 16.38888889 = -3.097177673 x = -3.097177673 Simplifying x = -3.097177673Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.874955453, -3.097177673}
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