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Simplifying x2 + 5x + -1525 = 0 Reorder the terms: -1525 + 5x + x2 = 0 Solving -1525 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1525' to each side of the equation. -1525 + 5x + 1525 + x2 = 0 + 1525 Reorder the terms: -1525 + 1525 + 5x + x2 = 0 + 1525 Combine like terms: -1525 + 1525 = 0 0 + 5x + x2 = 0 + 1525 5x + x2 = 0 + 1525 Combine like terms: 0 + 1525 = 1525 5x + x2 = 1525 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 = 1525 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1525 + 6.25 Combine like terms: 1525 + 6.25 = 1531.25 6.25 + 5x + x2 = 1531.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1531.25 Calculate the square root of the right side: 39.131189606 Break this problem into two subproblems by setting (x + 2.5) equal to 39.131189606 and -39.131189606.Subproblem 1
x + 2.5 = 39.131189606 Simplifying x + 2.5 = 39.131189606 Reorder the terms: 2.5 + x = 39.131189606 Solving 2.5 + x = 39.131189606 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 = 39.131189606 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 39.131189606 + -2.5 x = 39.131189606 + -2.5 Combine like terms: 39.131189606 + -2.5 = 36.631189606 x = 36.631189606 Simplifying x = 36.631189606Subproblem 2
x + 2.5 = -39.131189606 Simplifying x + 2.5 = -39.131189606 Reorder the terms: 2.5 + x = -39.131189606 Solving 2.5 + x = -39.131189606 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 = -39.131189606 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -39.131189606 + -2.5 x = -39.131189606 + -2.5 Combine like terms: -39.131189606 + -2.5 = -41.631189606 x = -41.631189606 Simplifying x = -41.631189606Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.631189606, -41.631189606}
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