Solve Using the Square Root Property 3(x+5)^2-72=0

$3 {(x + 5)}^{2} - 72 = 0$

Step 1

Simplify $3 {(x + 5)}^{2} - 72$ .

Simplify each term.

Rewrite ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$3 ((x + 5) (x + 5)) - 72 = 0$

Expand $(x + 5) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$3 (x (x + 5) + 5 (x + 5)) - 72 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 5 + 5 (x + 5)) - 72 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5) - 72 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x \cdot 5 + 5 x + 5 \cdot 5) - 72 = 0$

Move $5$ to the left of $x$ .

$3 (x^{2} + 5 \cdot x + 5 x + 5 \cdot 5) - 72 = 0$

Multiply $5$ by $5$ .

$3 (x^{2} + 5 x + 5 x + 25) - 72 = 0$

Add $5 x$ and $5 x$ .

$3 (x^{2} + 10 x + 25) - 72 = 0$

Apply the distributive property.

$3 x^{2} + 3 (10 x) + 3 \cdot 25 - 72 = 0$

Simplify.

Multiply $10$ by $3$ .

$3 x^{2} + 30 x + 3 \cdot 25 - 72 = 0$

Multiply $3$ by $25$ .

$3 x^{2} + 30 x + 75 - 72 = 0$

Subtract $72$ from $75$ .

$3 x^{2} + 30 x + 3 = 0$

Step 2

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

$x = - 5 - 2 \sqrt{6}, - 5 + 2 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - 5 - 2 \sqrt{6}, - 5 + 2 \sqrt{6}$

Decimal Form:

$x = - 9.89897948 \dots, - 0.10102051 \dots$

Step 4