Solve for u 2u^2+2u+24=(u-3)^2

$2 u^{2} + 2 u + 24 = {(u - 3)}^{2}$

Step 1

Simplify ${(u - 3)}^{2}$ .

Rewrite.

$2 u^{2} + 2 u + 24 = 0 + 0 + {(u - 3)}^{2}$

Rewrite ${(u - 3)}^{2}$ as $(u - 3) (u - 3)$ .

$2 u^{2} + 2 u + 24 = (u - 3) (u - 3)$

Expand $(u - 3) (u - 3)$ using the FOIL Method.

Apply the distributive property.

$2 u^{2} + 2 u + 24 = u (u - 3) - 3 (u - 3)$

Apply the distributive property.

$2 u^{2} + 2 u + 24 = u \cdot u + u \cdot - 3 - 3 (u - 3)$

Apply the distributive property.

$2 u^{2} + 2 u + 24 = u \cdot u + u \cdot - 3 - 3 u - 3 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

Multiply $u$ by $u$ .

$2 u^{2} + 2 u + 24 = u^{2} + u \cdot - 3 - 3 u - 3 \cdot - 3$

Move $- 3$ to the left of $u$ .

$2 u^{2} + 2 u + 24 = u^{2} - 3 \cdot u - 3 u - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$2 u^{2} + 2 u + 24 = u^{2} - 3 u - 3 u + 9$

Subtract $3 u$ from $- 3 u$ .

$2 u^{2} + 2 u + 24 = u^{2} - 6 u + 9$

Step 2

Move all terms containing $u$ to the left side of the equation.

Subtract $u^{2}$ from both sides of the equation.

$2 u^{2} + 2 u + 24 - u^{2} = - 6 u + 9$

Add $6 u$ to both sides of the equation.

$2 u^{2} + 2 u + 24 - u^{2} + 6 u = 9$

Subtract $u^{2}$ from $2 u^{2}$ .

$u^{2} + 2 u + 24 + 6 u = 9$

Add $2 u$ and $6 u$ .

$u^{2} + 8 u + 24 = 9$

Step 3

Subtract $9$ from both sides of the equation.

$u^{2} + 8 u + 24 - 9 = 0$

Step 4

Subtract $9$ from $24$ .

$u^{2} + 8 u + 15 = 0$

Step 5

Factor $u^{2} + 8 u + 15$ 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 $15$ and whose sum is $8$ .

$3, 5$

Write the factored form using these integers.

$(u + 3) (u + 5) = 0$

Step 6

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

$u + 3 = 0$

$u + 5 = 0$

Step 7

Set $u + 3$ equal to $0$ and solve for $u$ .

Set $u + 3$ equal to $0$ .

$u + 3 = 0$

Subtract $3$ from both sides of the equation.

$u = - 3$

Step 8

Set $u + 5$ equal to $0$ and solve for $u$ .

Set $u + 5$ equal to $0$ .

$u + 5 = 0$

Subtract $5$ from both sides of the equation.

$u = - 5$

Step 9

The final solution is all the values that make $(u + 3) (u + 5) = 0$ true.

$u = - 3, - 5$

Solve for u 2u^2+2u+24=(u-3)^2

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