Solve 3(x+5)*3(x+5)=3

$$3 ( x + 5 ) \cdot 3 ( x + 5 ) = 3$$

Solve for x

$$x=\frac{\sqrt{3}}{3}-5\approx -4.422649731$$

$$x=-\frac{\sqrt{3}}{3}-5\approx -5.577350269$$

Steps Using the Quadratic Formula

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

$$3\left(x+5\right)^{2}\times 3=3$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$3\left(x^{2}+10x+25\right)\times 3=3$$

Multiply 3 and 3 to get 9.

$$9\left(x^{2}+10x+25\right)=3$$

Use the distributive property to multiply 9 by x^{2}+10x+25.

$$9x^{2}+90x+225=3$$

Subtract 3 from both sides.

$$9x^{2}+90x+225-3=0$$

Subtract 3 from 225 to get 222.

$$9x^{2}+90x+222=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 90 for b, and 222 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-90±\sqrt{90^{2}-4\times 9\times 222}}{2\times 9}$$

Square 90.

$$x=\frac{-90±\sqrt{8100-4\times 9\times 222}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{-90±\sqrt{8100-36\times 222}}{2\times 9}$$

Multiply -36 times 222.

$$x=\frac{-90±\sqrt{8100-7992}}{2\times 9}$$

Add 8100 to -7992.

$$x=\frac{-90±\sqrt{108}}{2\times 9}$$

Take the square root of 108.

$$x=\frac{-90±6\sqrt{3}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{-90±6\sqrt{3}}{18}$$

Now solve the equation x=\frac{-90±6\sqrt{3}}{18} when ± is plus. Add -90 to 6\sqrt{3}.

$$x=\frac{6\sqrt{3}-90}{18}$$

Divide -90+6\sqrt{3} by 18.

$$x=\frac{\sqrt{3}}{3}-5$$

Now solve the equation x=\frac{-90±6\sqrt{3}}{18} when ± is minus. Subtract 6\sqrt{3} from -90.

$$x=\frac{-6\sqrt{3}-90}{18}$$

Divide -90-6\sqrt{3} by 18.

$$x=-\frac{\sqrt{3}}{3}-5$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{3}-5 x=-\frac{\sqrt{3}}{3}-5$$

Steps for Completing the Square

Multiply x+5 and x+5 to get \left(x+5\right)^{2}.

$$3\left(x+5\right)^{2}\times 3=3$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$3\left(x^{2}+10x+25\right)\times 3=3$$

Multiply 3 and 3 to get 9.

$$9\left(x^{2}+10x+25\right)=3$$

Use the distributive property to multiply 9 by x^{2}+10x+25.

$$9x^{2}+90x+225=3$$

Subtract 225 from both sides.

$$9x^{2}+90x=3-225$$

Subtract 225 from 3 to get -222.

$$9x^{2}+90x=-222$$

Divide both sides by 9.

$$\frac{9x^{2}+90x}{9}=-\frac{222}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x^{2}+\frac{90}{9}x=-\frac{222}{9}$$

Divide 90 by 9.

$$x^{2}+10x=-\frac{222}{9}$$

Reduce the fraction \frac{-222}{9} to lowest terms by extracting and canceling out 3.

$$x^{2}+10x=-\frac{74}{3}$$

Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+10x+5^{2}=-\frac{74}{3}+5^{2}$$

Square 5.

$$x^{2}+10x+25=-\frac{74}{3}+25$$

Add -\frac{74}{3} to 25.

$$x^{2}+10x+25=\frac{1}{3}$$

Factor x^{2}+10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+5\right)^{2}=\frac{1}{3}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{\frac{1}{3}}$$

Simplify.

$$x+5=\frac{\sqrt{3}}{3} x+5=-\frac{\sqrt{3}}{3}$$

Subtract 5 from both sides of the equation.

$$x=\frac{\sqrt{3}}{3}-5 x=-\frac{\sqrt{3}}{3}-5$$