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Simplifying x2 + x + -3200 = 0 Reorder the terms: -3200 + x + x2 = 0 Solving -3200 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3200' to each side of the equation. -3200 + x + 3200 + x2 = 0 + 3200 Reorder the terms: -3200 + 3200 + x + x2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + x + x2 = 0 + 3200 x + x2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 x + x2 = 3200 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3200 + 0.25 Reorder the terms: 0.25 + x + x2 = 3200 + 0.25 Combine like terms: 3200 + 0.25 = 3200.25 0.25 + x + x2 = 3200.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3200.25 Calculate the square root of the right side: 56.57075216 Break this problem into two subproblems by setting (x + 0.5) equal to 56.57075216 and -56.57075216.Subproblem 1
x + 0.5 = 56.57075216 Simplifying x + 0.5 = 56.57075216 Reorder the terms: 0.5 + x = 56.57075216 Solving 0.5 + x = 56.57075216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 56.57075216 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 56.57075216 + -0.5 x = 56.57075216 + -0.5 Combine like terms: 56.57075216 + -0.5 = 56.07075216 x = 56.07075216 Simplifying x = 56.07075216Subproblem 2
x + 0.5 = -56.57075216 Simplifying x + 0.5 = -56.57075216 Reorder the terms: 0.5 + x = -56.57075216 Solving 0.5 + x = -56.57075216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -56.57075216 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -56.57075216 + -0.5 x = -56.57075216 + -0.5 Combine like terms: -56.57075216 + -0.5 = -57.07075216 x = -57.07075216 Simplifying x = -57.07075216Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.07075216, -57.07075216}
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