(X-15)(X-15)=36

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Solution for (X-15)(X-15)=36 equation:


Simplifying
(X + -15)(X + -15) = 36

Reorder the terms:
(-15 + X)(X + -15) = 36

Reorder the terms:
(-15 + X)(-15 + X) = 36

Multiply (-15 + X) * (-15 + X)
(-15(-15 + X) + X(-15 + X)) = 36
((-15 * -15 + X * -15) + X(-15 + X)) = 36
((225 + -15X) + X(-15 + X)) = 36
(225 + -15X + (-15 * X + X * X)) = 36
(225 + -15X + (-15X + X2)) = 36

Combine like terms: -15X + -15X = -30X
(225 + -30X + X2) = 36

Solving
225 + -30X + X2 = 36

Solving for variable 'X'.

Reorder the terms:
225 + -36 + -30X + X2 = 36 + -36

Combine like terms: 225 + -36 = 189
189 + -30X + X2 = 36 + -36

Combine like terms: 36 + -36 = 0
189 + -30X + X2 = 0

Factor a trinomial.
(9 + -1X)(21 + -1X) = 0

Subproblem 1

Set the factor '(9 + -1X)' equal to zero and attempt to solve: Simplifying 9 + -1X = 0 Solving 9 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1X = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1X = 0 + -9 -1X = 0 + -9 Combine like terms: 0 + -9 = -9 -1X = -9 Divide each side by '-1'. X = 9 Simplifying X = 9

Subproblem 2

Set the factor '(21 + -1X)' equal to zero and attempt to solve: Simplifying 21 + -1X = 0 Solving 21 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1X = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1X = 0 + -21 -1X = 0 + -21 Combine like terms: 0 + -21 = -21 -1X = -21 Divide each side by '-1'. X = 21 Simplifying X = 21

Solution

X = {9, 21}

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