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Simplifying x2 + x + -224 = 0 Reorder the terms: -224 + x + x2 = 0 Solving -224 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + x + x2 = 0 + 224 x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 x + x2 = 224 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 = 224 + 0.25 Reorder the terms: 0.25 + x + x2 = 224 + 0.25 Combine like terms: 224 + 0.25 = 224.25 0.25 + x + x2 = 224.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 224.25 Calculate the square root of the right side: 14.974979132 Break this problem into two subproblems by setting (x + 0.5) equal to 14.974979132 and -14.974979132.Subproblem 1
x + 0.5 = 14.974979132 Simplifying x + 0.5 = 14.974979132 Reorder the terms: 0.5 + x = 14.974979132 Solving 0.5 + x = 14.974979132 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 = 14.974979132 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.974979132 + -0.5 x = 14.974979132 + -0.5 Combine like terms: 14.974979132 + -0.5 = 14.474979132 x = 14.474979132 Simplifying x = 14.474979132Subproblem 2
x + 0.5 = -14.974979132 Simplifying x + 0.5 = -14.974979132 Reorder the terms: 0.5 + x = -14.974979132 Solving 0.5 + x = -14.974979132 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 = -14.974979132 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.974979132 + -0.5 x = -14.974979132 + -0.5 Combine like terms: -14.974979132 + -0.5 = -15.474979132 x = -15.474979132 Simplifying x = -15.474979132Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.474979132, -15.474979132}
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