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Simplifying 9x2 + 37x + -4 = 0 Reorder the terms: -4 + 37x + 9x2 = 0 Solving -4 + 37x + 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'. -0.4444444444 + 4.111111111x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 4.111111111x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 4.111111111x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 4.111111111x + x2 = 0 + 0.4444444444 4.111111111x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 4.111111111x + x2 = 0.4444444444 The x term is 4.111111111x. Take half its coefficient (2.055555556). Square it (4.225308644) and add it to both sides. Add '4.225308644' to each side of the equation. 4.111111111x + 4.225308644 + x2 = 0.4444444444 + 4.225308644 Reorder the terms: 4.225308644 + 4.111111111x + x2 = 0.4444444444 + 4.225308644 Combine like terms: 0.4444444444 + 4.225308644 = 4.6697530884 4.225308644 + 4.111111111x + x2 = 4.6697530884 Factor a perfect square on the left side: (x + 2.055555556)(x + 2.055555556) = 4.6697530884 Calculate the square root of the right side: 2.160961149 Break this problem into two subproblems by setting (x + 2.055555556) equal to 2.160961149 and -2.160961149.Subproblem 1
x + 2.055555556 = 2.160961149 Simplifying x + 2.055555556 = 2.160961149 Reorder the terms: 2.055555556 + x = 2.160961149 Solving 2.055555556 + x = 2.160961149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + x = 2.160961149 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + x = 2.160961149 + -2.055555556 x = 2.160961149 + -2.055555556 Combine like terms: 2.160961149 + -2.055555556 = 0.105405593 x = 0.105405593 Simplifying x = 0.105405593Subproblem 2
x + 2.055555556 = -2.160961149 Simplifying x + 2.055555556 = -2.160961149 Reorder the terms: 2.055555556 + x = -2.160961149 Solving 2.055555556 + x = -2.160961149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.055555556' to each side of the equation. 2.055555556 + -2.055555556 + x = -2.160961149 + -2.055555556 Combine like terms: 2.055555556 + -2.055555556 = 0.000000000 0.000000000 + x = -2.160961149 + -2.055555556 x = -2.160961149 + -2.055555556 Combine like terms: -2.160961149 + -2.055555556 = -4.216516705 x = -4.216516705 Simplifying x = -4.216516705Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.105405593, -4.216516705}
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