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Simplifying 13X2 + 12X + -32 = 0 Reorder the terms: -32 + 12X + 13X2 = 0 Solving -32 + 12X + 13X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.461538462 + 0.9230769231X + X2 = 0 Move the constant term to the right: Add '2.461538462' to each side of the equation. -2.461538462 + 0.9230769231X + 2.461538462 + X2 = 0 + 2.461538462 Reorder the terms: -2.461538462 + 2.461538462 + 0.9230769231X + X2 = 0 + 2.461538462 Combine like terms: -2.461538462 + 2.461538462 = 0.000000000 0.000000000 + 0.9230769231X + X2 = 0 + 2.461538462 0.9230769231X + X2 = 0 + 2.461538462 Combine like terms: 0 + 2.461538462 = 2.461538462 0.9230769231X + X2 = 2.461538462 The X term is 0.9230769231X. Take half its coefficient (0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. 0.9230769231X + 0.2130177515 + X2 = 2.461538462 + 0.2130177515 Reorder the terms: 0.2130177515 + 0.9230769231X + X2 = 2.461538462 + 0.2130177515 Combine like terms: 2.461538462 + 0.2130177515 = 2.6745562135 0.2130177515 + 0.9230769231X + X2 = 2.6745562135 Factor a perfect square on the left side: (X + 0.4615384616)(X + 0.4615384616) = 2.6745562135 Calculate the square root of the right side: 1.635407048 Break this problem into two subproblems by setting (X + 0.4615384616) equal to 1.635407048 and -1.635407048.Subproblem 1
X + 0.4615384616 = 1.635407048 Simplifying X + 0.4615384616 = 1.635407048 Reorder the terms: 0.4615384616 + X = 1.635407048 Solving 0.4615384616 + X = 1.635407048 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + X = 1.635407048 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + X = 1.635407048 + -0.4615384616 X = 1.635407048 + -0.4615384616 Combine like terms: 1.635407048 + -0.4615384616 = 1.1738685864 X = 1.1738685864 Simplifying X = 1.1738685864Subproblem 2
X + 0.4615384616 = -1.635407048 Simplifying X + 0.4615384616 = -1.635407048 Reorder the terms: 0.4615384616 + X = -1.635407048 Solving 0.4615384616 + X = -1.635407048 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + X = -1.635407048 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + X = -1.635407048 + -0.4615384616 X = -1.635407048 + -0.4615384616 Combine like terms: -1.635407048 + -0.4615384616 = -2.0969455096 X = -2.0969455096 Simplifying X = -2.0969455096Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.1738685864, -2.0969455096}
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