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Simplifying x2 + 128x + 3250 = 0 Reorder the terms: 3250 + 128x + x2 = 0 Solving 3250 + 128x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3250' to each side of the equation. 3250 + 128x + -3250 + x2 = 0 + -3250 Reorder the terms: 3250 + -3250 + 128x + x2 = 0 + -3250 Combine like terms: 3250 + -3250 = 0 0 + 128x + x2 = 0 + -3250 128x + x2 = 0 + -3250 Combine like terms: 0 + -3250 = -3250 128x + x2 = -3250 The x term is 128x. Take half its coefficient (64). Square it (4096) and add it to both sides. Add '4096' to each side of the equation. 128x + 4096 + x2 = -3250 + 4096 Reorder the terms: 4096 + 128x + x2 = -3250 + 4096 Combine like terms: -3250 + 4096 = 846 4096 + 128x + x2 = 846 Factor a perfect square on the left side: (x + 64)(x + 64) = 846 Calculate the square root of the right side: 29.086079144 Break this problem into two subproblems by setting (x + 64) equal to 29.086079144 and -29.086079144.Subproblem 1
x + 64 = 29.086079144 Simplifying x + 64 = 29.086079144 Reorder the terms: 64 + x = 29.086079144 Solving 64 + x = 29.086079144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = 29.086079144 + -64 Combine like terms: 64 + -64 = 0 0 + x = 29.086079144 + -64 x = 29.086079144 + -64 Combine like terms: 29.086079144 + -64 = -34.913920856 x = -34.913920856 Simplifying x = -34.913920856Subproblem 2
x + 64 = -29.086079144 Simplifying x + 64 = -29.086079144 Reorder the terms: 64 + x = -29.086079144 Solving 64 + x = -29.086079144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + x = -29.086079144 + -64 Combine like terms: 64 + -64 = 0 0 + x = -29.086079144 + -64 x = -29.086079144 + -64 Combine like terms: -29.086079144 + -64 = -93.086079144 x = -93.086079144 Simplifying x = -93.086079144Solution
The solution to the problem is based on the solutions from the subproblems. x = {-34.913920856, -93.086079144}
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