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Simplifying x(x + 6) = 2880 Reorder the terms: x(6 + x) = 2880 (6 * x + x * x) = 2880 (6x + x2) = 2880 Solving 6x + x2 = 2880 Solving for variable 'x'. Reorder the terms: -2880 + 6x + x2 = 2880 + -2880 Combine like terms: 2880 + -2880 = 0 -2880 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2880' to each side of the equation. -2880 + 6x + 2880 + x2 = 0 + 2880 Reorder the terms: -2880 + 2880 + 6x + x2 = 0 + 2880 Combine like terms: -2880 + 2880 = 0 0 + 6x + x2 = 0 + 2880 6x + x2 = 0 + 2880 Combine like terms: 0 + 2880 = 2880 6x + x2 = 2880 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2880 + 9 Reorder the terms: 9 + 6x + x2 = 2880 + 9 Combine like terms: 2880 + 9 = 2889 9 + 6x + x2 = 2889 Factor a perfect square on the left side: (x + 3)(x + 3) = 2889 Calculate the square root of the right side: 53.749418602 Break this problem into two subproblems by setting (x + 3) equal to 53.749418602 and -53.749418602.Subproblem 1
x + 3 = 53.749418602 Simplifying x + 3 = 53.749418602 Reorder the terms: 3 + x = 53.749418602 Solving 3 + x = 53.749418602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 53.749418602 + -3 Combine like terms: 3 + -3 = 0 0 + x = 53.749418602 + -3 x = 53.749418602 + -3 Combine like terms: 53.749418602 + -3 = 50.749418602 x = 50.749418602 Simplifying x = 50.749418602Subproblem 2
x + 3 = -53.749418602 Simplifying x + 3 = -53.749418602 Reorder the terms: 3 + x = -53.749418602 Solving 3 + x = -53.749418602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -53.749418602 + -3 Combine like terms: 3 + -3 = 0 0 + x = -53.749418602 + -3 x = -53.749418602 + -3 Combine like terms: -53.749418602 + -3 = -56.749418602 x = -56.749418602 Simplifying x = -56.749418602Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.749418602, -56.749418602}
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