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Simplifying x(x + 1) = 48294792 Reorder the terms: x(1 + x) = 48294792 (1 * x + x * x) = 48294792 (1x + x2) = 48294792 Solving 1x + x2 = 48294792 Solving for variable 'x'. Reorder the terms: -48294792 + 1x + x2 = 48294792 + -48294792 Combine like terms: 48294792 + -48294792 = 0 -48294792 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48294792' to each side of the equation. -48294792 + 1x + 48294792 + x2 = 0 + 48294792 Reorder the terms: -48294792 + 48294792 + 1x + x2 = 0 + 48294792 Combine like terms: -48294792 + 48294792 = 0 0 + 1x + x2 = 0 + 48294792 1x + x2 = 0 + 48294792 Combine like terms: 0 + 48294792 = 48294792 1x + x2 = 48294792 The x term is 1x. 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 = 48294792 + 0.25 Reorder the terms: 0.25 + x + x2 = 48294792 + 0.25 Combine like terms: 48294792 + 0.25 = 48294792.25 0.25 + x + x2 = 48294792.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 48294792.25 Calculate the square root of the right side: 6949.445463488 Break this problem into two subproblems by setting (x + 0.5) equal to 6949.445463488 and -6949.445463488.Subproblem 1
x + 0.5 = 6949.445463488 Simplifying x + 0.5 = 6949.445463488 Reorder the terms: 0.5 + x = 6949.445463488 Solving 0.5 + x = 6949.445463488 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 = 6949.445463488 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6949.445463488 + -0.5 x = 6949.445463488 + -0.5 Combine like terms: 6949.445463488 + -0.5 = 6948.945463488 x = 6948.945463488 Simplifying x = 6948.945463488Subproblem 2
x + 0.5 = -6949.445463488 Simplifying x + 0.5 = -6949.445463488 Reorder the terms: 0.5 + x = -6949.445463488 Solving 0.5 + x = -6949.445463488 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 = -6949.445463488 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6949.445463488 + -0.5 x = -6949.445463488 + -0.5 Combine like terms: -6949.445463488 + -0.5 = -6949.945463488 x = -6949.945463488 Simplifying x = -6949.945463488Solution
The solution to the problem is based on the solutions from the subproblems. x = {6948.945463488, -6949.945463488}
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