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Simplifying x2 + 6x + -3600 = 0 Reorder the terms: -3600 + 6x + x2 = 0 Solving -3600 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 6x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 6x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 6x + x2 = 0 + 3600 6x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 6x + x2 = 3600 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 = 3600 + 9 Reorder the terms: 9 + 6x + x2 = 3600 + 9 Combine like terms: 3600 + 9 = 3609 9 + 6x + x2 = 3609 Factor a perfect square on the left side: (x + 3)(x + 3) = 3609 Calculate the square root of the right side: 60.074953184 Break this problem into two subproblems by setting (x + 3) equal to 60.074953184 and -60.074953184.Subproblem 1
x + 3 = 60.074953184 Simplifying x + 3 = 60.074953184 Reorder the terms: 3 + x = 60.074953184 Solving 3 + x = 60.074953184 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 = 60.074953184 + -3 Combine like terms: 3 + -3 = 0 0 + x = 60.074953184 + -3 x = 60.074953184 + -3 Combine like terms: 60.074953184 + -3 = 57.074953184 x = 57.074953184 Simplifying x = 57.074953184Subproblem 2
x + 3 = -60.074953184 Simplifying x + 3 = -60.074953184 Reorder the terms: 3 + x = -60.074953184 Solving 3 + x = -60.074953184 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 = -60.074953184 + -3 Combine like terms: 3 + -3 = 0 0 + x = -60.074953184 + -3 x = -60.074953184 + -3 Combine like terms: -60.074953184 + -3 = -63.074953184 x = -63.074953184 Simplifying x = -63.074953184Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.074953184, -63.074953184}
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