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Simplifying X(X + 4) = 75 Reorder the terms: X(4 + X) = 75 (4 * X + X * X) = 75 (4X + X2) = 75 Solving 4X + X2 = 75 Solving for variable 'X'. Reorder the terms: -75 + 4X + X2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 4X + 75 + X2 = 0 + 75 Reorder the terms: -75 + 75 + 4X + X2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 4X + X2 = 0 + 75 4X + X2 = 0 + 75 Combine like terms: 0 + 75 = 75 4X + X2 = 75 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 = 75 + 4 Reorder the terms: 4 + 4X + X2 = 75 + 4 Combine like terms: 75 + 4 = 79 4 + 4X + X2 = 79 Factor a perfect square on the left side: (X + 2)(X + 2) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (X + 2) equal to 8.888194417 and -8.888194417.Subproblem 1
X + 2 = 8.888194417 Simplifying X + 2 = 8.888194417 Reorder the terms: 2 + X = 8.888194417 Solving 2 + X = 8.888194417 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 = 8.888194417 + -2 Combine like terms: 2 + -2 = 0 0 + X = 8.888194417 + -2 X = 8.888194417 + -2 Combine like terms: 8.888194417 + -2 = 6.888194417 X = 6.888194417 Simplifying X = 6.888194417Subproblem 2
X + 2 = -8.888194417 Simplifying X + 2 = -8.888194417 Reorder the terms: 2 + X = -8.888194417 Solving 2 + X = -8.888194417 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 = -8.888194417 + -2 Combine like terms: 2 + -2 = 0 0 + X = -8.888194417 + -2 X = -8.888194417 + -2 Combine like terms: -8.888194417 + -2 = -10.888194417 X = -10.888194417 Simplifying X = -10.888194417Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.888194417, -10.888194417}
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