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Simplifying (X + 7)(X + -9) = 195 Reorder the terms: (7 + X)(X + -9) = 195 Reorder the terms: (7 + X)(-9 + X) = 195 Multiply (7 + X) * (-9 + X) (7(-9 + X) + X(-9 + X)) = 195 ((-9 * 7 + X * 7) + X(-9 + X)) = 195 ((-63 + 7X) + X(-9 + X)) = 195 (-63 + 7X + (-9 * X + X * X)) = 195 (-63 + 7X + (-9X + X2)) = 195 Combine like terms: 7X + -9X = -2X (-63 + -2X + X2) = 195 Solving -63 + -2X + X2 = 195 Solving for variable 'X'. Reorder the terms: -63 + -195 + -2X + X2 = 195 + -195 Combine like terms: -63 + -195 = -258 -258 + -2X + X2 = 195 + -195 Combine like terms: 195 + -195 = 0 -258 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '258' to each side of the equation. -258 + -2X + 258 + X2 = 0 + 258 Reorder the terms: -258 + 258 + -2X + X2 = 0 + 258 Combine like terms: -258 + 258 = 0 0 + -2X + X2 = 0 + 258 -2X + X2 = 0 + 258 Combine like terms: 0 + 258 = 258 -2X + X2 = 258 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 = 258 + 1 Reorder the terms: 1 + -2X + X2 = 258 + 1 Combine like terms: 258 + 1 = 259 1 + -2X + X2 = 259 Factor a perfect square on the left side: (X + -1)(X + -1) = 259 Calculate the square root of the right side: 16.093476939 Break this problem into two subproblems by setting (X + -1) equal to 16.093476939 and -16.093476939.Subproblem 1
X + -1 = 16.093476939 Simplifying X + -1 = 16.093476939 Reorder the terms: -1 + X = 16.093476939 Solving -1 + X = 16.093476939 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 = 16.093476939 + 1 Combine like terms: -1 + 1 = 0 0 + X = 16.093476939 + 1 X = 16.093476939 + 1 Combine like terms: 16.093476939 + 1 = 17.093476939 X = 17.093476939 Simplifying X = 17.093476939Subproblem 2
X + -1 = -16.093476939 Simplifying X + -1 = -16.093476939 Reorder the terms: -1 + X = -16.093476939 Solving -1 + X = -16.093476939 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 = -16.093476939 + 1 Combine like terms: -1 + 1 = 0 0 + X = -16.093476939 + 1 X = -16.093476939 + 1 Combine like terms: -16.093476939 + 1 = -15.093476939 X = -15.093476939 Simplifying X = -15.093476939Solution
The solution to the problem is based on the solutions from the subproblems. X = {17.093476939, -15.093476939}
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