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Simplifying (x + 2)(x + 4) = 84 Reorder the terms: (2 + x)(x + 4) = 84 Reorder the terms: (2 + x)(4 + x) = 84 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 84 ((4 * 2 + x * 2) + x(4 + x)) = 84 ((8 + 2x) + x(4 + x)) = 84 (8 + 2x + (4 * x + x * x)) = 84 (8 + 2x + (4x + x2)) = 84 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 84 Solving 8 + 6x + x2 = 84 Solving for variable 'x'. Reorder the terms: 8 + -84 + 6x + x2 = 84 + -84 Combine like terms: 8 + -84 = -76 -76 + 6x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -76 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 6x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 6x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 6x + x2 = 0 + 76 6x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 6x + x2 = 76 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 = 76 + 9 Reorder the terms: 9 + 6x + x2 = 76 + 9 Combine like terms: 76 + 9 = 85 9 + 6x + x2 = 85 Factor a perfect square on the left side: (x + 3)(x + 3) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + 3) equal to 9.219544457 and -9.219544457.Subproblem 1
x + 3 = 9.219544457 Simplifying x + 3 = 9.219544457 Reorder the terms: 3 + x = 9.219544457 Solving 3 + x = 9.219544457 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 = 9.219544457 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.219544457 + -3 x = 9.219544457 + -3 Combine like terms: 9.219544457 + -3 = 6.219544457 x = 6.219544457 Simplifying x = 6.219544457Subproblem 2
x + 3 = -9.219544457 Simplifying x + 3 = -9.219544457 Reorder the terms: 3 + x = -9.219544457 Solving 3 + x = -9.219544457 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 = -9.219544457 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.219544457 + -3 x = -9.219544457 + -3 Combine like terms: -9.219544457 + -3 = -12.219544457 x = -12.219544457 Simplifying x = -12.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.219544457, -12.219544457}
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