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Simplifying (X)(X + 4) = 149 Reorder the terms: X(4 + X) = 149 (4 * X + X * X) = 149 (4X + X2) = 149 Solving 4X + X2 = 149 Solving for variable 'X'. Reorder the terms: -149 + 4X + X2 = 149 + -149 Combine like terms: 149 + -149 = 0 -149 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '149' to each side of the equation. -149 + 4X + 149 + X2 = 0 + 149 Reorder the terms: -149 + 149 + 4X + X2 = 0 + 149 Combine like terms: -149 + 149 = 0 0 + 4X + X2 = 0 + 149 4X + X2 = 0 + 149 Combine like terms: 0 + 149 = 149 4X + X2 = 149 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 = 149 + 4 Reorder the terms: 4 + 4X + X2 = 149 + 4 Combine like terms: 149 + 4 = 153 4 + 4X + X2 = 153 Factor a perfect square on the left side: (X + 2)(X + 2) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (X + 2) equal to 12.369316877 and -12.369316877.Subproblem 1
X + 2 = 12.369316877 Simplifying X + 2 = 12.369316877 Reorder the terms: 2 + X = 12.369316877 Solving 2 + X = 12.369316877 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 = 12.369316877 + -2 Combine like terms: 2 + -2 = 0 0 + X = 12.369316877 + -2 X = 12.369316877 + -2 Combine like terms: 12.369316877 + -2 = 10.369316877 X = 10.369316877 Simplifying X = 10.369316877Subproblem 2
X + 2 = -12.369316877 Simplifying X + 2 = -12.369316877 Reorder the terms: 2 + X = -12.369316877 Solving 2 + X = -12.369316877 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 = -12.369316877 + -2 Combine like terms: 2 + -2 = 0 0 + X = -12.369316877 + -2 X = -12.369316877 + -2 Combine like terms: -12.369316877 + -2 = -14.369316877 X = -14.369316877 Simplifying X = -14.369316877Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.369316877, -14.369316877}
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