Solve for y (y-2)^2-10(y-2)+9=0

${(y - 2)}^{2} - 10 (y - 2) + 9 = 0$

Step 1

Factor the left side of the equation.

Let $u = y - 2$ . Substitute $u$ for all occurrences of $y - 2$ .

$u^{2} - 10 u + 9 = 0$

Factor $u^{2} - 10 u + 9$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $9$ and whose sum is $- 10$ .

$- 9, - 1$

Write the factored form using these integers.

$(u - 9) (u - 1) = 0$

Replace all occurrences of $u$ with $y - 2$ .

$(y - 2 - 9) (y - 2 - 1) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 2 - 9 = 0$

$y - 2 - 1 = 0$

Step 3

Set $y - 2 - 9$ equal to $0$ and solve for $y$ .

Set $y - 2 - 9$ equal to $0$ .

$y - 2 - 9 = 0$

Solve $y - 2 - 9 = 0$ for $y$ .

Subtract $9$ from $- 2$ .

$y - 11 = 0$

Add $11$ to both sides of the equation.

$y = 11$

Step 4

Set $y - 2 - 1$ equal to $0$ and solve for $y$ .

Set $y - 2 - 1$ equal to $0$ .

$y - 2 - 1 = 0$

Solve $y - 2 - 1 = 0$ for $y$ .

Subtract $1$ from $- 2$ .

$y - 3 = 0$

Add $3$ to both sides of the equation.

$y = 3$

Step 5

The final solution is all the values that make $(y - 2 - 9) (y - 2 - 1) = 0$ true.

$y = 11, 3$

Solve for y (y-2)^2-10(y-2)+9=0

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