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Simplifying X(8 + -1X) = 14 (8 * X + -1X * X) = 14 (8X + -1X2) = 14 Solving 8X + -1X2 = 14 Solving for variable 'X'. Reorder the terms: -14 + 8X + -1X2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 8X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -8X + X2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8X + -14 + X2 = 0 + -14 Reorder the terms: 14 + -14 + -8X + X2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8X + X2 = 0 + -14 -8X + X2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8X + X2 = -14 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = -14 + 16 Reorder the terms: 16 + -8X + X2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8X + X2 = 2 Factor a perfect square on the left side: (X + -4)(X + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (X + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
X + -4 = 1.414213562 Simplifying X + -4 = 1.414213562 Reorder the terms: -4 + X = 1.414213562 Solving -4 + X = 1.414213562 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + X = 1.414213562 + 4 X = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 X = 5.414213562 Simplifying X = 5.414213562Subproblem 2
X + -4 = -1.414213562 Simplifying X + -4 = -1.414213562 Reorder the terms: -4 + X = -1.414213562 Solving -4 + X = -1.414213562 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + X = -1.414213562 + 4 X = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 X = 2.585786438 Simplifying X = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.414213562, 2.585786438}
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