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Simplifying X(X + 2) = 37 + 6(X + X + 2) Reorder the terms: X(2 + X) = 37 + 6(X + X + 2) (2 * X + X * X) = 37 + 6(X + X + 2) (2X + X2) = 37 + 6(X + X + 2) Reorder the terms: 2X + X2 = 37 + 6(2 + X + X) Combine like terms: X + X = 2X 2X + X2 = 37 + 6(2 + 2X) 2X + X2 = 37 + (2 * 6 + 2X * 6) 2X + X2 = 37 + (12 + 12X) Combine like terms: 37 + 12 = 49 2X + X2 = 49 + 12X Solving 2X + X2 = 49 + 12X Solving for variable 'X'. Reorder the terms: -49 + 2X + -12X + X2 = 49 + 12X + -49 + -12X Combine like terms: 2X + -12X = -10X -49 + -10X + X2 = 49 + 12X + -49 + -12X Reorder the terms: -49 + -10X + X2 = 49 + -49 + 12X + -12X Combine like terms: 49 + -49 = 0 -49 + -10X + X2 = 0 + 12X + -12X -49 + -10X + X2 = 12X + -12X Combine like terms: 12X + -12X = 0 -49 + -10X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -10X + 49 + X2 = 0 + 49 Reorder the terms: -49 + 49 + -10X + X2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -10X + X2 = 0 + 49 -10X + X2 = 0 + 49 Combine like terms: 0 + 49 = 49 -10X + X2 = 49 The X term is -10X. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10X + 25 + X2 = 49 + 25 Reorder the terms: 25 + -10X + X2 = 49 + 25 Combine like terms: 49 + 25 = 74 25 + -10X + X2 = 74 Factor a perfect square on the left side: (X + -5)(X + -5) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (X + -5) equal to 8.602325267 and -8.602325267.Subproblem 1
X + -5 = 8.602325267 Simplifying X + -5 = 8.602325267 Reorder the terms: -5 + X = 8.602325267 Solving -5 + X = 8.602325267 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + X = 8.602325267 + 5 Combine like terms: -5 + 5 = 0 0 + X = 8.602325267 + 5 X = 8.602325267 + 5 Combine like terms: 8.602325267 + 5 = 13.602325267 X = 13.602325267 Simplifying X = 13.602325267Subproblem 2
X + -5 = -8.602325267 Simplifying X + -5 = -8.602325267 Reorder the terms: -5 + X = -8.602325267 Solving -5 + X = -8.602325267 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + X = -8.602325267 + 5 Combine like terms: -5 + 5 = 0 0 + X = -8.602325267 + 5 X = -8.602325267 + 5 Combine like terms: -8.602325267 + 5 = -3.602325267 X = -3.602325267 Simplifying X = -3.602325267Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.602325267, -3.602325267}
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