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Simplifying (X + -5)(X + -7) + -9 = 0 Reorder the terms: (-5 + X)(X + -7) + -9 = 0 Reorder the terms: (-5 + X)(-7 + X) + -9 = 0 Multiply (-5 + X) * (-7 + X) (-5(-7 + X) + X(-7 + X)) + -9 = 0 ((-7 * -5 + X * -5) + X(-7 + X)) + -9 = 0 ((35 + -5X) + X(-7 + X)) + -9 = 0 (35 + -5X + (-7 * X + X * X)) + -9 = 0 (35 + -5X + (-7X + X2)) + -9 = 0 Combine like terms: -5X + -7X = -12X (35 + -12X + X2) + -9 = 0 Reorder the terms: 35 + -9 + -12X + X2 = 0 Combine like terms: 35 + -9 = 26 26 + -12X + X2 = 0 Solving 26 + -12X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -12X + -26 + X2 = 0 + -26 Reorder the terms: 26 + -26 + -12X + X2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -12X + X2 = 0 + -26 -12X + X2 = 0 + -26 Combine like terms: 0 + -26 = -26 -12X + X2 = -26 The X term is -12X. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12X + 36 + X2 = -26 + 36 Reorder the terms: 36 + -12X + X2 = -26 + 36 Combine like terms: -26 + 36 = 10 36 + -12X + X2 = 10 Factor a perfect square on the left side: (X + -6)(X + -6) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (X + -6) equal to 3.16227766 and -3.16227766.Subproblem 1
X + -6 = 3.16227766 Simplifying X + -6 = 3.16227766 Reorder the terms: -6 + X = 3.16227766 Solving -6 + X = 3.16227766 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = 3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + X = 3.16227766 + 6 X = 3.16227766 + 6 Combine like terms: 3.16227766 + 6 = 9.16227766 X = 9.16227766 Simplifying X = 9.16227766Subproblem 2
X + -6 = -3.16227766 Simplifying X + -6 = -3.16227766 Reorder the terms: -6 + X = -3.16227766 Solving -6 + X = -3.16227766 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = -3.16227766 + 6 Combine like terms: -6 + 6 = 0 0 + X = -3.16227766 + 6 X = -3.16227766 + 6 Combine like terms: -3.16227766 + 6 = 2.83772234 X = 2.83772234 Simplifying X = 2.83772234Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.16227766, 2.83772234}
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