Solve (3.84x-0.48)*(3x+4)=30

$$(3.84x-0.48) \times (3x+4)=30$$

Solve for x

$$x=-2.375$$

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3.84x-0.48 by 3x+4 and combine like terms.

$$11.52x^{2}+13.92x-1.92=30$$

Subtract 30 from both sides.

$$11.52x^{2}+13.92x-1.92-30=0$$

Subtract 30 from -1.92 to get -31.92.

$$11.52x^{2}+13.92x-31.92=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11.52 for a, 13.92 for b, and -31.92 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-13.92±\sqrt{13.92^{2}-4\times 11.52\left(-31.92\right)}}{2\times 11.52}$$

Square 13.92 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-13.92±\sqrt{193.7664-4\times 11.52\left(-31.92\right)}}{2\times 11.52}$$

Multiply -4 times 11.52.

$$x=\frac{-13.92±\sqrt{193.7664-46.08\left(-31.92\right)}}{2\times 11.52}$$

Multiply -46.08 times -31.92 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-13.92±\sqrt{\frac{121104+919296}{625}}}{2\times 11.52}$$

Add 193.7664 to 1470.8736 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-13.92±\sqrt{1664.64}}{2\times 11.52}$$

Take the square root of 1664.64.

$$x=\frac{-13.92±\frac{204}{5}}{2\times 11.52}$$

Multiply 2 times 11.52.

$$x=\frac{-13.92±\frac{204}{5}}{23.04}$$

Now solve the equation x=\frac{-13.92±\frac{204}{5}}{23.04} when ± is plus. Add -13.92 to \frac{204}{5} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{672}{25}}{23.04}$$

Divide \frac{672}{25} by 23.04 by multiplying \frac{672}{25} by the reciprocal of 23.04.

$$x=\frac{7}{6}$$

Now solve the equation x=\frac{-13.92±\frac{204}{5}}{23.04} when ± is minus. Subtract \frac{204}{5} from -13.92 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{1368}{25}}{23.04}$$

Divide -\frac{1368}{25} by 23.04 by multiplying -\frac{1368}{25} by the reciprocal of 23.04.

$$x=-\frac{19}{8}$$

The equation is now solved.

$$x=\frac{7}{6} x=-\frac{19}{8}$$

Steps for Completing the Square

Use the distributive property to multiply 3.84x-0.48 by 3x+4 and combine like terms.

$$11.52x^{2}+13.92x-1.92=30$$

Add 1.92 to both sides.

$$11.52x^{2}+13.92x=30+1.92$$

Add 30 and 1.92 to get 31.92.

$$11.52x^{2}+13.92x=31.92$$

Divide both sides of the equation by 11.52, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{11.52x^{2}+13.92x}{11.52}=\frac{31.92}{11.52}$$

Dividing by 11.52 undoes the multiplication by 11.52.

$$x^{2}+\frac{13.92}{11.52}x=\frac{31.92}{11.52}$$

Divide 13.92 by 11.52 by multiplying 13.92 by the reciprocal of 11.52.

$$x^{2}+\frac{29}{24}x=\frac{31.92}{11.52}$$

Divide 31.92 by 11.52 by multiplying 31.92 by the reciprocal of 11.52.

$$x^{2}+\frac{29}{24}x=\frac{133}{48}$$

Divide \frac{29}{24}, the coefficient of the x term, by 2 to get \frac{29}{48}. Then add the square of \frac{29}{48} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{29}{24}x+\frac{29}{48}^{2}=\frac{133}{48}+\frac{29}{48}^{2}$$

Square \frac{29}{48} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{29}{24}x+\frac{841}{2304}=\frac{133}{48}+\frac{841}{2304}$$

Add \frac{133}{48} to \frac{841}{2304} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{29}{24}x+\frac{841}{2304}=\frac{7225}{2304}$$

Factor x^{2}+\frac{29}{24}x+\frac{841}{2304}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{29}{48}\right)^{2}=\frac{7225}{2304}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{29}{48}\right)^{2}}=\sqrt{\frac{7225}{2304}}$$

Simplify.

$$x+\frac{29}{48}=\frac{85}{48} x+\frac{29}{48}=-\frac{85}{48}$$

Subtract \frac{29}{48} from both sides of the equation.

$$x=\frac{7}{6} x=-\frac{19}{8}$$