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Simplifying x2 + 8x + -2880 = 0 Reorder the terms: -2880 + 8x + x2 = 0 Solving -2880 + 8x + 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 + 8x + 2880 + x2 = 0 + 2880 Reorder the terms: -2880 + 2880 + 8x + x2 = 0 + 2880 Combine like terms: -2880 + 2880 = 0 0 + 8x + x2 = 0 + 2880 8x + x2 = 0 + 2880 Combine like terms: 0 + 2880 = 2880 8x + x2 = 2880 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 2880 + 16 Reorder the terms: 16 + 8x + x2 = 2880 + 16 Combine like terms: 2880 + 16 = 2896 16 + 8x + x2 = 2896 Factor a perfect square on the left side: (x + 4)(x + 4) = 2896 Calculate the square root of the right side: 53.814496188 Break this problem into two subproblems by setting (x + 4) equal to 53.814496188 and -53.814496188.Subproblem 1
x + 4 = 53.814496188 Simplifying x + 4 = 53.814496188 Reorder the terms: 4 + x = 53.814496188 Solving 4 + x = 53.814496188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 53.814496188 + -4 Combine like terms: 4 + -4 = 0 0 + x = 53.814496188 + -4 x = 53.814496188 + -4 Combine like terms: 53.814496188 + -4 = 49.814496188 x = 49.814496188 Simplifying x = 49.814496188Subproblem 2
x + 4 = -53.814496188 Simplifying x + 4 = -53.814496188 Reorder the terms: 4 + x = -53.814496188 Solving 4 + x = -53.814496188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -53.814496188 + -4 Combine like terms: 4 + -4 = 0 0 + x = -53.814496188 + -4 x = -53.814496188 + -4 Combine like terms: -53.814496188 + -4 = -57.814496188 x = -57.814496188 Simplifying x = -57.814496188Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.814496188, -57.814496188}
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