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Simplifying x2 + 15x + -540 = 0 Reorder the terms: -540 + 15x + x2 = 0 Solving -540 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + 15x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + 15x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 15x + x2 = 0 + 540 15x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 15x + x2 = 540 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 540 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 540 + 56.25 Combine like terms: 540 + 56.25 = 596.25 56.25 + 15x + x2 = 596.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 596.25 Calculate the square root of the right side: 24.418230894 Break this problem into two subproblems by setting (x + 7.5) equal to 24.418230894 and -24.418230894.Subproblem 1
x + 7.5 = 24.418230894 Simplifying x + 7.5 = 24.418230894 Reorder the terms: 7.5 + x = 24.418230894 Solving 7.5 + x = 24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 24.418230894 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 24.418230894 + -7.5 x = 24.418230894 + -7.5 Combine like terms: 24.418230894 + -7.5 = 16.918230894 x = 16.918230894 Simplifying x = 16.918230894Subproblem 2
x + 7.5 = -24.418230894 Simplifying x + 7.5 = -24.418230894 Reorder the terms: 7.5 + x = -24.418230894 Solving 7.5 + x = -24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -24.418230894 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -24.418230894 + -7.5 x = -24.418230894 + -7.5 Combine like terms: -24.418230894 + -7.5 = -31.918230894 x = -31.918230894 Simplifying x = -31.918230894Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.918230894, -31.918230894}
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