Solve for u 2u^2+7u-24=(u+2)^2

$2 u^{2} + 7 u - 24 = {(u + 2)}^{2}$

Step 1

Simplify ${(u + 2)}^{2}$ .

Rewrite.

$2 u^{2} + 7 u - 24 = 0 + 0 + {(u + 2)}^{2}$

Rewrite ${(u + 2)}^{2}$ as $(u + 2) (u + 2)$ .

$2 u^{2} + 7 u - 24 = (u + 2) (u + 2)$

Expand $(u + 2) (u + 2)$ using the FOIL Method.

Apply the distributive property.

$2 u^{2} + 7 u - 24 = u (u + 2) + 2 (u + 2)$

Apply the distributive property.

$2 u^{2} + 7 u - 24 = u \cdot u + u \cdot 2 + 2 (u + 2)$

Apply the distributive property.

$2 u^{2} + 7 u - 24 = u \cdot u + u \cdot 2 + 2 u + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Multiply $u$ by $u$ .

$2 u^{2} + 7 u - 24 = u^{2} + u \cdot 2 + 2 u + 2 \cdot 2$

Move $2$ to the left of $u$ .

$2 u^{2} + 7 u - 24 = u^{2} + 2 \cdot u + 2 u + 2 \cdot 2$

Multiply $2$ by $2$ .

$2 u^{2} + 7 u - 24 = u^{2} + 2 u + 2 u + 4$

Add $2 u$ and $2 u$ .

$2 u^{2} + 7 u - 24 = u^{2} + 4 u + 4$

Step 2

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

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

$2 u^{2} + 7 u - 24 - u^{2} = 4 u + 4$

Subtract $4 u$ from both sides of the equation.

$2 u^{2} + 7 u - 24 - u^{2} - 4 u = 4$

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

$u^{2} + 7 u - 24 - 4 u = 4$

Subtract $4 u$ from $7 u$ .

$u^{2} + 3 u - 24 = 4$

Step 3

Subtract $4$ from both sides of the equation.

$u^{2} + 3 u - 24 - 4 = 0$

Step 4

Subtract $4$ from $- 24$ .

$u^{2} + 3 u - 28 = 0$

Step 5

Factor $u^{2} + 3 u - 28$ 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 $- 28$ and whose sum is $3$ .

$- 4, 7$

Write the factored form using these integers.

$(u - 4) (u + 7) = 0$

Step 6

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

$u - 4 = 0$

$u + 7 = 0$

Step 7

Set $u - 4$ equal to $0$ and solve for $u$ .

Set $u - 4$ equal to $0$ .

$u - 4 = 0$

Add $4$ to both sides of the equation.

$u = 4$

Step 8

Set $u + 7$ equal to $0$ and solve for $u$ .

Set $u + 7$ equal to $0$ .

$u + 7 = 0$

Subtract $7$ from both sides of the equation.

$u = - 7$

Step 9

The final solution is all the values that make $(u - 4) (u + 7) = 0$ true.

$u = 4, - 7$

Solve for u 2u^2+7u-24=(u+2)^2

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