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Simplifying -3.6x2 + 9x + 4 = 0 Reorder the terms: 4 + 9x + -3.6x2 = 0 Solving 4 + 9x + -3.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.6 the coefficient of the squared term: Divide each side by '-3.6'. -1.111111111 + -2.5x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -2.5x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -2.5x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 1.111111111 -2.5x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -2.5x + x2 = 1.111111111 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1.111111111 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1.111111111 + 1.5625 Combine like terms: 1.111111111 + 1.5625 = 2.673611111 1.5625 + -2.5x + x2 = 2.673611111 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.673611111 Calculate the square root of the right side: 1.635118072 Break this problem into two subproblems by setting (x + -1.25) equal to 1.635118072 and -1.635118072.Subproblem 1
x + -1.25 = 1.635118072 Simplifying x + -1.25 = 1.635118072 Reorder the terms: -1.25 + x = 1.635118072 Solving -1.25 + x = 1.635118072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.635118072 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.635118072 + 1.25 x = 1.635118072 + 1.25 Combine like terms: 1.635118072 + 1.25 = 2.885118072 x = 2.885118072 Simplifying x = 2.885118072Subproblem 2
x + -1.25 = -1.635118072 Simplifying x + -1.25 = -1.635118072 Reorder the terms: -1.25 + x = -1.635118072 Solving -1.25 + x = -1.635118072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.635118072 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.635118072 + 1.25 x = -1.635118072 + 1.25 Combine like terms: -1.635118072 + 1.25 = -0.385118072 x = -0.385118072 Simplifying x = -0.385118072Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.885118072, -0.385118072}
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