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Simplifying (x + 7)(x + -1) = 16 Reorder the terms: (7 + x)(x + -1) = 16 Reorder the terms: (7 + x)(-1 + x) = 16 Multiply (7 + x) * (-1 + x) (7(-1 + x) + x(-1 + x)) = 16 ((-1 * 7 + x * 7) + x(-1 + x)) = 16 ((-7 + 7x) + x(-1 + x)) = 16 (-7 + 7x + (-1 * x + x * x)) = 16 (-7 + 7x + (-1x + x2)) = 16 Combine like terms: 7x + -1x = 6x (-7 + 6x + x2) = 16 Solving -7 + 6x + x2 = 16 Solving for variable 'x'. Reorder the terms: -7 + -16 + 6x + x2 = 16 + -16 Combine like terms: -7 + -16 = -23 -23 + 6x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -23 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 6x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 6x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 6x + x2 = 0 + 23 6x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 6x + x2 = 23 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 = 23 + 9 Reorder the terms: 9 + 6x + x2 = 23 + 9 Combine like terms: 23 + 9 = 32 9 + 6x + x2 = 32 Factor a perfect square on the left side: (x + 3)(x + 3) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 3) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 3 = 5.656854249 Simplifying x + 3 = 5.656854249 Reorder the terms: 3 + x = 5.656854249 Solving 3 + x = 5.656854249 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 = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.656854249 + -3 x = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 x = 2.656854249 Simplifying x = 2.656854249Subproblem 2
x + 3 = -5.656854249 Simplifying x + 3 = -5.656854249 Reorder the terms: 3 + x = -5.656854249 Solving 3 + x = -5.656854249 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 = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.656854249 + -3 x = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 x = -8.656854249 Simplifying x = -8.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.656854249, -8.656854249}
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