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Simplifying (x)(x + 6) = 540 Reorder the terms: x(6 + x) = 540 (6 * x + x * x) = 540 (6x + x2) = 540 Solving 6x + x2 = 540 Solving for variable 'x'. Reorder the terms: -540 + 6x + x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -540 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + 6x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + 6x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 6x + x2 = 0 + 540 6x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 6x + x2 = 540 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 = 540 + 9 Reorder the terms: 9 + 6x + x2 = 540 + 9 Combine like terms: 540 + 9 = 549 9 + 6x + x2 = 549 Factor a perfect square on the left side: (x + 3)(x + 3) = 549 Calculate the square root of the right side: 23.430749028 Break this problem into two subproblems by setting (x + 3) equal to 23.430749028 and -23.430749028.Subproblem 1
x + 3 = 23.430749028 Simplifying x + 3 = 23.430749028 Reorder the terms: 3 + x = 23.430749028 Solving 3 + x = 23.430749028 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 = 23.430749028 + -3 Combine like terms: 3 + -3 = 0 0 + x = 23.430749028 + -3 x = 23.430749028 + -3 Combine like terms: 23.430749028 + -3 = 20.430749028 x = 20.430749028 Simplifying x = 20.430749028Subproblem 2
x + 3 = -23.430749028 Simplifying x + 3 = -23.430749028 Reorder the terms: 3 + x = -23.430749028 Solving 3 + x = -23.430749028 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 = -23.430749028 + -3 Combine like terms: 3 + -3 = 0 0 + x = -23.430749028 + -3 x = -23.430749028 + -3 Combine like terms: -23.430749028 + -3 = -26.430749028 x = -26.430749028 Simplifying x = -26.430749028Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.430749028, -26.430749028}
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