Solve Using the Square Root Property 3(x+4)^2-24=0

$3 {(x + 4)}^{2} - 24 = 0$

Step 1

Simplify $3 {(x + 4)}^{2} - 24$ .

Simplify each term.

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$3 ((x + 4) (x + 4)) - 24 = 0$

Expand $(x + 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$3 (x (x + 4) + 4 (x + 4)) - 24 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 4 + 4 (x + 4)) - 24 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4) - 24 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x \cdot 4 + 4 x + 4 \cdot 4) - 24 = 0$

Move $4$ to the left of $x$ .

$3 (x^{2} + 4 \cdot x + 4 x + 4 \cdot 4) - 24 = 0$

Multiply $4$ by $4$ .

$3 (x^{2} + 4 x + 4 x + 16) - 24 = 0$

Add $4 x$ and $4 x$ .

$3 (x^{2} + 8 x + 16) - 24 = 0$

Apply the distributive property.

$3 x^{2} + 3 (8 x) + 3 \cdot 16 - 24 = 0$

Simplify.

Multiply $8$ by $3$ .

$3 x^{2} + 24 x + 3 \cdot 16 - 24 = 0$

Multiply $3$ by $16$ .

$3 x^{2} + 24 x + 48 - 24 = 0$

Subtract $24$ from $48$ .

$3 x^{2} + 24 x + 24 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 4 - 2 \sqrt{2}, - 4 + 2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - 4 - 2 \sqrt{2}, - 4 + 2 \sqrt{2}$

Decimal Form:

$x = - 6.82842712 \dots, - 1.17157287 \dots$

Step 4