Solve Using the Quadratic Formula 3(x+5)^2=60

$3 {(x + 5)}^{2} = 60$

Move all terms to the left side of the equation and simplify.

Subtract $60$ from both sides of the equation.

$3 {(x + 5)}^{2} - 60 = 0$

Simplify $3 {(x + 5)}^{2} - 60$ .

Simplify each term.

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

$3 ((x + 5) (x + 5)) - 60 = 0$

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

Apply the distributive property.

$3 (x (x + 5) + 5 (x + 5)) - 60 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 5 + 5 (x + 5)) - 60 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5) - 60 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x \cdot 5 + 5 x + 5 \cdot 5) - 60 = 0$

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

$3 (x^{2} + 5 \cdot x + 5 x + 5 \cdot 5) - 60 = 0$

Multiply $5$ by $5$ .

$3 (x^{2} + 5 x + 5 x + 25) - 60 = 0$

Add $5 x$ and $5 x$ .

$3 (x^{2} + 10 x + 25) - 60 = 0$

Apply the distributive property.

$3 x^{2} + 3 (10 x) + 3 \cdot 25 - 60 = 0$

Simplify.

Multiply $10$ by $3$ .

$3 x^{2} + 30 x + 3 \cdot 25 - 60 = 0$

Multiply $3$ by $25$ .

$3 x^{2} + 30 x + 75 - 60 = 0$

Subtract $60$ from $75$ .

$3 x^{2} + 30 x + 15 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = 30$ , and $c = 15$ into the quadratic formula and solve for $x$ .

$\frac{- 30 \pm \sqrt{30^{2} - 4 \cdot (3 \cdot 15)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $30$ to the power of $2$ .

$x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 3 \cdot 15}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{- 30 \pm \sqrt{900 - 12 \cdot 15}}{2 \cdot 3}$

Multiply $- 12$ by $15$ .

$x = \frac{- 30 \pm \sqrt{900 - 180}}{2 \cdot 3}$

Subtract $180$ from $900$ .

$x = \frac{- 30 \pm \sqrt{720}}{2 \cdot 3}$

Rewrite $720$ as $12^{2} \cdot 5$ .

Factor $144$ out of $720$ .

$x = \frac{- 30 \pm \sqrt{144 (5)}}{2 \cdot 3}$

Rewrite $144$ as $12^{2}$ .

$x = \frac{- 30 \pm \sqrt{12^{2} \cdot 5}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 30 \pm 12 \sqrt{5}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 30 \pm 12 \sqrt{5}}{6}$

Simplify $\frac{- 30 \pm 12 \sqrt{5}}{6}$ .

$x = - 5 \pm 2 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$x = - 5 \pm 2 \sqrt{5}$

Decimal Form:

$x = - 0.52786404 \dots, - 9.47213595 \dots$

Solve Using the Quadratic Formula 3(x+5)^2=60

Related Questions

Support LCMGCF.com by disabling your adblocker.