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Simplifying x2 + 12x + -3000 = 0 Reorder the terms: -3000 + 12x + x2 = 0 Solving -3000 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 12x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 12x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 12x + x2 = 0 + 3000 12x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 12x + x2 = 3000 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 = 3000 + 36 Reorder the terms: 36 + 12x + x2 = 3000 + 36 Combine like terms: 3000 + 36 = 3036 36 + 12x + x2 = 3036 Factor a perfect square on the left side: (x + 6)(x + 6) = 3036 Calculate the square root of the right side: 55.099909256 Break this problem into two subproblems by setting (x + 6) equal to 55.099909256 and -55.099909256.Subproblem 1
x + 6 = 55.099909256 Simplifying x + 6 = 55.099909256 Reorder the terms: 6 + x = 55.099909256 Solving 6 + x = 55.099909256 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 = 55.099909256 + -6 Combine like terms: 6 + -6 = 0 0 + x = 55.099909256 + -6 x = 55.099909256 + -6 Combine like terms: 55.099909256 + -6 = 49.099909256 x = 49.099909256 Simplifying x = 49.099909256Subproblem 2
x + 6 = -55.099909256 Simplifying x + 6 = -55.099909256 Reorder the terms: 6 + x = -55.099909256 Solving 6 + x = -55.099909256 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 = -55.099909256 + -6 Combine like terms: 6 + -6 = 0 0 + x = -55.099909256 + -6 x = -55.099909256 + -6 Combine like terms: -55.099909256 + -6 = -61.099909256 x = -61.099909256 Simplifying x = -61.099909256Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.099909256, -61.099909256}
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