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Simplifying x2 + -5x + -10000000 = 0 Reorder the terms: -10000000 + -5x + x2 = 0 Solving -10000000 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000000' to each side of the equation. -10000000 + -5x + 10000000 + x2 = 0 + 10000000 Reorder the terms: -10000000 + 10000000 + -5x + x2 = 0 + 10000000 Combine like terms: -10000000 + 10000000 = 0 0 + -5x + x2 = 0 + 10000000 -5x + x2 = 0 + 10000000 Combine like terms: 0 + 10000000 = 10000000 -5x + x2 = 10000000 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 10000000 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 10000000 + 6.25 Combine like terms: 10000000 + 6.25 = 10000006.25 6.25 + -5x + x2 = 10000006.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10000006.25 Calculate the square root of the right side: 3162.27864838 Break this problem into two subproblems by setting (x + -2.5) equal to 3162.27864838 and -3162.27864838.Subproblem 1
x + -2.5 = 3162.27864838 Simplifying x + -2.5 = 3162.27864838 Reorder the terms: -2.5 + x = 3162.27864838 Solving -2.5 + x = 3162.27864838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3162.27864838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3162.27864838 + 2.5 x = 3162.27864838 + 2.5 Combine like terms: 3162.27864838 + 2.5 = 3164.77864838 x = 3164.77864838 Simplifying x = 3164.77864838Subproblem 2
x + -2.5 = -3162.27864838 Simplifying x + -2.5 = -3162.27864838 Reorder the terms: -2.5 + x = -3162.27864838 Solving -2.5 + x = -3162.27864838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3162.27864838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3162.27864838 + 2.5 x = -3162.27864838 + 2.5 Combine like terms: -3162.27864838 + 2.5 = -3159.77864838 x = -3159.77864838 Simplifying x = -3159.77864838Solution
The solution to the problem is based on the solutions from the subproblems. x = {3164.77864838, -3159.77864838}
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