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Simplifying (x + 6)(x + 8) = 400 Reorder the terms: (6 + x)(x + 8) = 400 Reorder the terms: (6 + x)(8 + x) = 400 Multiply (6 + x) * (8 + x) (6(8 + x) + x(8 + x)) = 400 ((8 * 6 + x * 6) + x(8 + x)) = 400 ((48 + 6x) + x(8 + x)) = 400 (48 + 6x + (8 * x + x * x)) = 400 (48 + 6x + (8x + x2)) = 400 Combine like terms: 6x + 8x = 14x (48 + 14x + x2) = 400 Solving 48 + 14x + x2 = 400 Solving for variable 'x'. Reorder the terms: 48 + -400 + 14x + x2 = 400 + -400 Combine like terms: 48 + -400 = -352 -352 + 14x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -352 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '352' to each side of the equation. -352 + 14x + 352 + x2 = 0 + 352 Reorder the terms: -352 + 352 + 14x + x2 = 0 + 352 Combine like terms: -352 + 352 = 0 0 + 14x + x2 = 0 + 352 14x + x2 = 0 + 352 Combine like terms: 0 + 352 = 352 14x + x2 = 352 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 352 + 49 Reorder the terms: 49 + 14x + x2 = 352 + 49 Combine like terms: 352 + 49 = 401 49 + 14x + x2 = 401 Factor a perfect square on the left side: (x + 7)(x + 7) = 401 Calculate the square root of the right side: 20.024984395 Break this problem into two subproblems by setting (x + 7) equal to 20.024984395 and -20.024984395.Subproblem 1
x + 7 = 20.024984395 Simplifying x + 7 = 20.024984395 Reorder the terms: 7 + x = 20.024984395 Solving 7 + x = 20.024984395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 20.024984395 + -7 Combine like terms: 7 + -7 = 0 0 + x = 20.024984395 + -7 x = 20.024984395 + -7 Combine like terms: 20.024984395 + -7 = 13.024984395 x = 13.024984395 Simplifying x = 13.024984395Subproblem 2
x + 7 = -20.024984395 Simplifying x + 7 = -20.024984395 Reorder the terms: 7 + x = -20.024984395 Solving 7 + x = -20.024984395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -20.024984395 + -7 Combine like terms: 7 + -7 = 0 0 + x = -20.024984395 + -7 x = -20.024984395 + -7 Combine like terms: -20.024984395 + -7 = -27.024984395 x = -27.024984395 Simplifying x = -27.024984395Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.024984395, -27.024984395}
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