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Simplifying (X + 5)(X + 1) = 20 Reorder the terms: (5 + X)(X + 1) = 20 Reorder the terms: (5 + X)(1 + X) = 20 Multiply (5 + X) * (1 + X) (5(1 + X) + X(1 + X)) = 20 ((1 * 5 + X * 5) + X(1 + X)) = 20 ((5 + 5X) + X(1 + X)) = 20 (5 + 5X + (1 * X + X * X)) = 20 (5 + 5X + (1X + X2)) = 20 Combine like terms: 5X + 1X = 6X (5 + 6X + X2) = 20 Solving 5 + 6X + X2 = 20 Solving for variable 'X'. Reorder the terms: 5 + -20 + 6X + X2 = 20 + -20 Combine like terms: 5 + -20 = -15 -15 + 6X + X2 = 20 + -20 Combine like terms: 20 + -20 = 0 -15 + 6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 6X + 15 + X2 = 0 + 15 Reorder the terms: -15 + 15 + 6X + X2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6X + X2 = 0 + 15 6X + X2 = 0 + 15 Combine like terms: 0 + 15 = 15 6X + X2 = 15 The X term is 6X. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6X + 9 + X2 = 15 + 9 Reorder the terms: 9 + 6X + X2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6X + X2 = 24 Factor a perfect square on the left side: (X + 3)(X + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (X + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
X + 3 = 4.898979486 Simplifying X + 3 = 4.898979486 Reorder the terms: 3 + X = 4.898979486 Solving 3 + X = 4.898979486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + X = 4.898979486 + -3 X = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 X = 1.898979486 Simplifying X = 1.898979486Subproblem 2
X + 3 = -4.898979486 Simplifying X + 3 = -4.898979486 Reorder the terms: 3 + X = -4.898979486 Solving 3 + X = -4.898979486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + X = -4.898979486 + -3 X = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 X = -7.898979486 Simplifying X = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.898979486, -7.898979486}
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