(X-5)(X-7)-9=

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Solution for (X-5)(X-7)-9= equation:


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 = 9.16227766

Subproblem 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 = 2.83772234

Solution

The solution to the problem is based on the solutions from the subproblems. X = {9.16227766, 2.83772234}

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