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Simplifying 9x2 + 25x = 16 + -4x Reorder the terms: 25x + 9x2 = 16 + -4x Solving 25x + 9x2 = 16 + -4x Solving for variable 'x'. Reorder the terms: -16 + 25x + 4x + 9x2 = 16 + -4x + -16 + 4x Combine like terms: 25x + 4x = 29x -16 + 29x + 9x2 = 16 + -4x + -16 + 4x Reorder the terms: -16 + 29x + 9x2 = 16 + -16 + -4x + 4x Combine like terms: 16 + -16 = 0 -16 + 29x + 9x2 = 0 + -4x + 4x -16 + 29x + 9x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -16 + 29x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 3.222222222x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 3.222222222x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 3.222222222x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 3.222222222x + x2 = 0 + 1.777777778 3.222222222x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 3.222222222x + x2 = 1.777777778 The x term is 3.222222222x. Take half its coefficient (1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. 3.222222222x + 2.595679012 + x2 = 1.777777778 + 2.595679012 Reorder the terms: 2.595679012 + 3.222222222x + x2 = 1.777777778 + 2.595679012 Combine like terms: 1.777777778 + 2.595679012 = 4.37345679 2.595679012 + 3.222222222x + x2 = 4.37345679 Factor a perfect square on the left side: (x + 1.611111111)(x + 1.611111111) = 4.37345679 Calculate the square root of the right side: 2.091281136 Break this problem into two subproblems by setting (x + 1.611111111) equal to 2.091281136 and -2.091281136.Subproblem 1
x + 1.611111111 = 2.091281136 Simplifying x + 1.611111111 = 2.091281136 Reorder the terms: 1.611111111 + x = 2.091281136 Solving 1.611111111 + x = 2.091281136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = 2.091281136 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = 2.091281136 + -1.611111111 x = 2.091281136 + -1.611111111 Combine like terms: 2.091281136 + -1.611111111 = 0.480170025 x = 0.480170025 Simplifying x = 0.480170025Subproblem 2
x + 1.611111111 = -2.091281136 Simplifying x + 1.611111111 = -2.091281136 Reorder the terms: 1.611111111 + x = -2.091281136 Solving 1.611111111 + x = -2.091281136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.611111111' to each side of the equation. 1.611111111 + -1.611111111 + x = -2.091281136 + -1.611111111 Combine like terms: 1.611111111 + -1.611111111 = 0.000000000 0.000000000 + x = -2.091281136 + -1.611111111 x = -2.091281136 + -1.611111111 Combine like terms: -2.091281136 + -1.611111111 = -3.702392247 x = -3.702392247 Simplifying x = -3.702392247Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.480170025, -3.702392247}
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