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Simplifying X(X + 4) = 113 Reorder the terms: X(4 + X) = 113 (4 * X + X * X) = 113 (4X + X2) = 113 Solving 4X + X2 = 113 Solving for variable 'X'. Reorder the terms: -113 + 4X + X2 = 113 + -113 Combine like terms: 113 + -113 = 0 -113 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '113' to each side of the equation. -113 + 4X + 113 + X2 = 0 + 113 Reorder the terms: -113 + 113 + 4X + X2 = 0 + 113 Combine like terms: -113 + 113 = 0 0 + 4X + X2 = 0 + 113 4X + X2 = 0 + 113 Combine like terms: 0 + 113 = 113 4X + X2 = 113 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 113 + 4 Reorder the terms: 4 + 4X + X2 = 113 + 4 Combine like terms: 113 + 4 = 117 4 + 4X + X2 = 117 Factor a perfect square on the left side: (X + 2)(X + 2) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (X + 2) equal to 10.816653826 and -10.816653826.Subproblem 1
X + 2 = 10.816653826 Simplifying X + 2 = 10.816653826 Reorder the terms: 2 + X = 10.816653826 Solving 2 + X = 10.816653826 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 10.816653826 + -2 Combine like terms: 2 + -2 = 0 0 + X = 10.816653826 + -2 X = 10.816653826 + -2 Combine like terms: 10.816653826 + -2 = 8.816653826 X = 8.816653826 Simplifying X = 8.816653826Subproblem 2
X + 2 = -10.816653826 Simplifying X + 2 = -10.816653826 Reorder the terms: 2 + X = -10.816653826 Solving 2 + X = -10.816653826 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -10.816653826 + -2 Combine like terms: 2 + -2 = 0 0 + X = -10.816653826 + -2 X = -10.816653826 + -2 Combine like terms: -10.816653826 + -2 = -12.816653826 X = -12.816653826 Simplifying X = -12.816653826Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.816653826, -12.816653826}
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