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Simplifying x2 + 5x + -2880 = 0 Reorder the terms: -2880 + 5x + x2 = 0 Solving -2880 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2880' to each side of the equation. -2880 + 5x + 2880 + x2 = 0 + 2880 Reorder the terms: -2880 + 2880 + 5x + x2 = 0 + 2880 Combine like terms: -2880 + 2880 = 0 0 + 5x + x2 = 0 + 2880 5x + x2 = 0 + 2880 Combine like terms: 0 + 2880 = 2880 5x + x2 = 2880 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 = 2880 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2880 + 6.25 Combine like terms: 2880 + 6.25 = 2886.25 6.25 + 5x + x2 = 2886.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2886.25 Calculate the square root of the right side: 53.723830839 Break this problem into two subproblems by setting (x + 2.5) equal to 53.723830839 and -53.723830839.Subproblem 1
x + 2.5 = 53.723830839 Simplifying x + 2.5 = 53.723830839 Reorder the terms: 2.5 + x = 53.723830839 Solving 2.5 + x = 53.723830839 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 = 53.723830839 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 53.723830839 + -2.5 x = 53.723830839 + -2.5 Combine like terms: 53.723830839 + -2.5 = 51.223830839 x = 51.223830839 Simplifying x = 51.223830839Subproblem 2
x + 2.5 = -53.723830839 Simplifying x + 2.5 = -53.723830839 Reorder the terms: 2.5 + x = -53.723830839 Solving 2.5 + x = -53.723830839 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 = -53.723830839 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -53.723830839 + -2.5 x = -53.723830839 + -2.5 Combine like terms: -53.723830839 + -2.5 = -56.223830839 x = -56.223830839 Simplifying x = -56.223830839Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.223830839, -56.223830839}
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