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Simplifying x(x + 2) + 4(3 + 10x) + 12x + 12 = 0 Reorder the terms: x(2 + x) + 4(3 + 10x) + 12x + 12 = 0 (2 * x + x * x) + 4(3 + 10x) + 12x + 12 = 0 (2x + x2) + 4(3 + 10x) + 12x + 12 = 0 2x + x2 + (3 * 4 + 10x * 4) + 12x + 12 = 0 2x + x2 + (12 + 40x) + 12x + 12 = 0 Reorder the terms: 12 + 12 + 2x + 40x + 12x + x2 = 0 Combine like terms: 12 + 12 = 24 24 + 2x + 40x + 12x + x2 = 0 Combine like terms: 2x + 40x = 42x 24 + 42x + 12x + x2 = 0 Combine like terms: 42x + 12x = 54x 24 + 54x + x2 = 0 Solving 24 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 54x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 54x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 54x + x2 = 0 + -24 54x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 54x + x2 = -24 The x term is 54x. Take half its coefficient (27). Square it (729) and add it to both sides. Add '729' to each side of the equation. 54x + 729 + x2 = -24 + 729 Reorder the terms: 729 + 54x + x2 = -24 + 729 Combine like terms: -24 + 729 = 705 729 + 54x + x2 = 705 Factor a perfect square on the left side: (x + 27)(x + 27) = 705 Calculate the square root of the right side: 26.551836095 Break this problem into two subproblems by setting (x + 27) equal to 26.551836095 and -26.551836095.Subproblem 1
x + 27 = 26.551836095 Simplifying x + 27 = 26.551836095 Reorder the terms: 27 + x = 26.551836095 Solving 27 + x = 26.551836095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 26.551836095 + -27 Combine like terms: 27 + -27 = 0 0 + x = 26.551836095 + -27 x = 26.551836095 + -27 Combine like terms: 26.551836095 + -27 = -0.448163905 x = -0.448163905 Simplifying x = -0.448163905Subproblem 2
x + 27 = -26.551836095 Simplifying x + 27 = -26.551836095 Reorder the terms: 27 + x = -26.551836095 Solving 27 + x = -26.551836095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -26.551836095 + -27 Combine like terms: 27 + -27 = 0 0 + x = -26.551836095 + -27 x = -26.551836095 + -27 Combine like terms: -26.551836095 + -27 = -53.551836095 x = -53.551836095 Simplifying x = -53.551836095Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.448163905, -53.551836095}
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