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Simplifying x2 + 12x + -504 = 0 Reorder the terms: -504 + 12x + x2 = 0 Solving -504 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '504' to each side of the equation. -504 + 12x + 504 + x2 = 0 + 504 Reorder the terms: -504 + 504 + 12x + x2 = 0 + 504 Combine like terms: -504 + 504 = 0 0 + 12x + x2 = 0 + 504 12x + x2 = 0 + 504 Combine like terms: 0 + 504 = 504 12x + x2 = 504 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 504 + 36 Reorder the terms: 36 + 12x + x2 = 504 + 36 Combine like terms: 504 + 36 = 540 36 + 12x + x2 = 540 Factor a perfect square on the left side: (x + 6)(x + 6) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (x + 6) equal to 23.237900077 and -23.237900077.Subproblem 1
x + 6 = 23.237900077 Simplifying x + 6 = 23.237900077 Reorder the terms: 6 + x = 23.237900077 Solving 6 + x = 23.237900077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 23.237900077 + -6 Combine like terms: 6 + -6 = 0 0 + x = 23.237900077 + -6 x = 23.237900077 + -6 Combine like terms: 23.237900077 + -6 = 17.237900077 x = 17.237900077 Simplifying x = 17.237900077Subproblem 2
x + 6 = -23.237900077 Simplifying x + 6 = -23.237900077 Reorder the terms: 6 + x = -23.237900077 Solving 6 + x = -23.237900077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -23.237900077 + -6 Combine like terms: 6 + -6 = 0 0 + x = -23.237900077 + -6 x = -23.237900077 + -6 Combine like terms: -23.237900077 + -6 = -29.237900077 x = -29.237900077 Simplifying x = -29.237900077Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.237900077, -29.237900077}
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