(x-2)(x-7)-k=0

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Solution for (x-2)(x-7)-k=0 equation:


Simplifying
(x + -2)(x + -7) + -1k = 0

Reorder the terms:
(-2 + x)(x + -7) + -1k = 0

Reorder the terms:
(-2 + x)(-7 + x) + -1k = 0

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) + -1k = 0
((-7 * -2 + x * -2) + x(-7 + x)) + -1k = 0
((14 + -2x) + x(-7 + x)) + -1k = 0
(14 + -2x + (-7 * x + x * x)) + -1k = 0
(14 + -2x + (-7x + x2)) + -1k = 0

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) + -1k = 0

Reorder the terms:
14 + -1k + -9x + x2 = 0

Solving
14 + -1k + -9x + x2 = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-14' to each side of the equation.
14 + -1k + -9x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -1k + -9x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1k + -9x + x2 = 0 + -14
-1k + -9x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-1k + -9x + x2 = -14

Add '9x' to each side of the equation.
-1k + -9x + 9x + x2 = -14 + 9x

Combine like terms: -9x + 9x = 0
-1k + 0 + x2 = -14 + 9x
-1k + x2 = -14 + 9x

Add '-1x2' to each side of the equation.
-1k + x2 + -1x2 = -14 + 9x + -1x2

Combine like terms: x2 + -1x2 = 0
-1k + 0 = -14 + 9x + -1x2
-1k = -14 + 9x + -1x2

Divide each side by '-1'.
k = 14 + -9x + x2

Simplifying
k = 14 + -9x + x2

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