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Simplifying (X + 3)(X + -5) = 16 Reorder the terms: (3 + X)(X + -5) = 16 Reorder the terms: (3 + X)(-5 + X) = 16 Multiply (3 + X) * (-5 + X) (3(-5 + X) + X(-5 + X)) = 16 ((-5 * 3 + X * 3) + X(-5 + X)) = 16 ((-15 + 3X) + X(-5 + X)) = 16 (-15 + 3X + (-5 * X + X * X)) = 16 (-15 + 3X + (-5X + X2)) = 16 Combine like terms: 3X + -5X = -2X (-15 + -2X + X2) = 16 Solving -15 + -2X + X2 = 16 Solving for variable 'X'. Reorder the terms: -15 + -16 + -2X + X2 = 16 + -16 Combine like terms: -15 + -16 = -31 -31 + -2X + X2 = 16 + -16 Combine like terms: 16 + -16 = 0 -31 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -2X + 31 + X2 = 0 + 31 Reorder the terms: -31 + 31 + -2X + X2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -2X + X2 = 0 + 31 -2X + X2 = 0 + 31 Combine like terms: 0 + 31 = 31 -2X + X2 = 31 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 31 + 1 Reorder the terms: 1 + -2X + X2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + -2X + X2 = 32 Factor a perfect square on the left side: (X + -1)(X + -1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (X + -1) equal to 5.656854249 and -5.656854249.Subproblem 1
X + -1 = 5.656854249 Simplifying X + -1 = 5.656854249 Reorder the terms: -1 + X = 5.656854249 Solving -1 + X = 5.656854249 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 5.656854249 + 1 Combine like terms: -1 + 1 = 0 0 + X = 5.656854249 + 1 X = 5.656854249 + 1 Combine like terms: 5.656854249 + 1 = 6.656854249 X = 6.656854249 Simplifying X = 6.656854249Subproblem 2
X + -1 = -5.656854249 Simplifying X + -1 = -5.656854249 Reorder the terms: -1 + X = -5.656854249 Solving -1 + X = -5.656854249 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -5.656854249 + 1 Combine like terms: -1 + 1 = 0 0 + X = -5.656854249 + 1 X = -5.656854249 + 1 Combine like terms: -5.656854249 + 1 = -4.656854249 X = -4.656854249 Simplifying X = -4.656854249Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.656854249, -4.656854249}
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