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Simplifying 2x2 + 9x + -32 = 0 Reorder the terms: -32 + 9x + 2x2 = 0 Solving -32 + 9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + 4.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 4.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 4.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4.5x + x2 = 0 + 16 4.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 4.5x + x2 = 16 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 16 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 16 + 5.0625 Combine like terms: 16 + 5.0625 = 21.0625 5.0625 + 4.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + 2.25) equal to 4.589389938 and -4.589389938.Subproblem 1
x + 2.25 = 4.589389938 Simplifying x + 2.25 = 4.589389938 Reorder the terms: 2.25 + x = 4.589389938 Solving 2.25 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.589389938 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.589389938 + -2.25 x = 4.589389938 + -2.25 Combine like terms: 4.589389938 + -2.25 = 2.339389938 x = 2.339389938 Simplifying x = 2.339389938Subproblem 2
x + 2.25 = -4.589389938 Simplifying x + 2.25 = -4.589389938 Reorder the terms: 2.25 + x = -4.589389938 Solving 2.25 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.589389938 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.589389938 + -2.25 x = -4.589389938 + -2.25 Combine like terms: -4.589389938 + -2.25 = -6.839389938 x = -6.839389938 Simplifying x = -6.839389938Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.339389938, -6.839389938}
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