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Simplifying x + x2 = 5000 Solving x + x2 = 5000 Solving for variable 'x'. Reorder the terms: -5000 + x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x + x2 = 0 + 5000 x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 x + x2 = 5000 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 = 5000 + 0.25 Reorder the terms: 0.25 + x + x2 = 5000 + 0.25 Combine like terms: 5000 + 0.25 = 5000.25 0.25 + x + x2 = 5000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5000.25 Calculate the square root of the right side: 70.712445864 Break this problem into two subproblems by setting (x + 0.5) equal to 70.712445864 and -70.712445864.Subproblem 1
x + 0.5 = 70.712445864 Simplifying x + 0.5 = 70.712445864 Reorder the terms: 0.5 + x = 70.712445864 Solving 0.5 + x = 70.712445864 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 = 70.712445864 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 70.712445864 + -0.5 x = 70.712445864 + -0.5 Combine like terms: 70.712445864 + -0.5 = 70.212445864 x = 70.212445864 Simplifying x = 70.212445864Subproblem 2
x + 0.5 = -70.712445864 Simplifying x + 0.5 = -70.712445864 Reorder the terms: 0.5 + x = -70.712445864 Solving 0.5 + x = -70.712445864 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 = -70.712445864 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -70.712445864 + -0.5 x = -70.712445864 + -0.5 Combine like terms: -70.712445864 + -0.5 = -71.212445864 x = -71.212445864 Simplifying x = -71.212445864Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.212445864, -71.212445864}
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