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Simplifying 2X2 + 4X + X = 26 Reorder the terms: 4X + X + 2X2 = 26 Combine like terms: 4X + X = 5X 5X + 2X2 = 26 Solving 5X + 2X2 = 26 Solving for variable 'X'. Reorder the terms: -26 + 5X + 2X2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 5X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + 2.5X + X2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 2.5X + 13 + X2 = 0 + 13 Reorder the terms: -13 + 13 + 2.5X + X2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2.5X + X2 = 0 + 13 2.5X + X2 = 0 + 13 Combine like terms: 0 + 13 = 13 2.5X + X2 = 13 The X term is 2.5X. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5X + 1.5625 + X2 = 13 + 1.5625 Reorder the terms: 1.5625 + 2.5X + X2 = 13 + 1.5625 Combine like terms: 13 + 1.5625 = 14.5625 1.5625 + 2.5X + X2 = 14.5625 Factor a perfect square on the left side: (X + 1.25)(X + 1.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (X + 1.25) equal to 3.816084381 and -3.816084381.Subproblem 1
X + 1.25 = 3.816084381 Simplifying X + 1.25 = 3.816084381 Reorder the terms: 1.25 + X = 3.816084381 Solving 1.25 + X = 3.816084381 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = 3.816084381 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = 3.816084381 + -1.25 X = 3.816084381 + -1.25 Combine like terms: 3.816084381 + -1.25 = 2.566084381 X = 2.566084381 Simplifying X = 2.566084381Subproblem 2
X + 1.25 = -3.816084381 Simplifying X + 1.25 = -3.816084381 Reorder the terms: 1.25 + X = -3.816084381 Solving 1.25 + X = -3.816084381 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = -3.816084381 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = -3.816084381 + -1.25 X = -3.816084381 + -1.25 Combine like terms: -3.816084381 + -1.25 = -5.066084381 X = -5.066084381 Simplifying X = -5.066084381Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.566084381, -5.066084381}
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