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Simplifying x2 + 5x + -3000 = 0 Reorder the terms: -3000 + 5x + x2 = 0 Solving -3000 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 5x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 5x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 5x + x2 = 0 + 3000 5x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 5x + x2 = 3000 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 = 3000 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 3000 + 6.25 Combine like terms: 3000 + 6.25 = 3006.25 6.25 + 5x + x2 = 3006.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 3006.25 Calculate the square root of the right side: 54.829280499 Break this problem into two subproblems by setting (x + 2.5) equal to 54.829280499 and -54.829280499.Subproblem 1
x + 2.5 = 54.829280499 Simplifying x + 2.5 = 54.829280499 Reorder the terms: 2.5 + x = 54.829280499 Solving 2.5 + x = 54.829280499 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 = 54.829280499 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 54.829280499 + -2.5 x = 54.829280499 + -2.5 Combine like terms: 54.829280499 + -2.5 = 52.329280499 x = 52.329280499 Simplifying x = 52.329280499Subproblem 2
x + 2.5 = -54.829280499 Simplifying x + 2.5 = -54.829280499 Reorder the terms: 2.5 + x = -54.829280499 Solving 2.5 + x = -54.829280499 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 = -54.829280499 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -54.829280499 + -2.5 x = -54.829280499 + -2.5 Combine like terms: -54.829280499 + -2.5 = -57.329280499 x = -57.329280499 Simplifying x = -57.329280499Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.329280499, -57.329280499}
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