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Simplifying x2 + 6x + -5184 = 0 Reorder the terms: -5184 + 6x + x2 = 0 Solving -5184 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5184' to each side of the equation. -5184 + 6x + 5184 + x2 = 0 + 5184 Reorder the terms: -5184 + 5184 + 6x + x2 = 0 + 5184 Combine like terms: -5184 + 5184 = 0 0 + 6x + x2 = 0 + 5184 6x + x2 = 0 + 5184 Combine like terms: 0 + 5184 = 5184 6x + x2 = 5184 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 = 5184 + 9 Reorder the terms: 9 + 6x + x2 = 5184 + 9 Combine like terms: 5184 + 9 = 5193 9 + 6x + x2 = 5193 Factor a perfect square on the left side: (x + 3)(x + 3) = 5193 Calculate the square root of the right side: 72.062472897 Break this problem into two subproblems by setting (x + 3) equal to 72.062472897 and -72.062472897.Subproblem 1
x + 3 = 72.062472897 Simplifying x + 3 = 72.062472897 Reorder the terms: 3 + x = 72.062472897 Solving 3 + x = 72.062472897 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 = 72.062472897 + -3 Combine like terms: 3 + -3 = 0 0 + x = 72.062472897 + -3 x = 72.062472897 + -3 Combine like terms: 72.062472897 + -3 = 69.062472897 x = 69.062472897 Simplifying x = 69.062472897Subproblem 2
x + 3 = -72.062472897 Simplifying x + 3 = -72.062472897 Reorder the terms: 3 + x = -72.062472897 Solving 3 + x = -72.062472897 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 = -72.062472897 + -3 Combine like terms: 3 + -3 = 0 0 + x = -72.062472897 + -3 x = -72.062472897 + -3 Combine like terms: -72.062472897 + -3 = -75.062472897 x = -75.062472897 Simplifying x = -75.062472897Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.062472897, -75.062472897}
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