Solve -1/12(x-4)^2+3=27/12

$$- \frac { 1 } { 12 } ( x - 4 ) ^ { 2 } + 3 = \frac { 27 } { 12 }$$

Solve for x

$$x=7$$

$$x=1$$

Steps by Finding Square Root

Subtract 3 from both sides of the equation.

$$-\frac{1}{12}\left(x-4\right)^{2}+3-3=\frac{9}{4}-3$$

Subtracting 3 from itself leaves 0.

$$-\frac{1}{12}\left(x-4\right)^{2}=\frac{9}{4}-3$$

Subtract 3 from \frac{9}{4}.

$$-\frac{1}{12}\left(x-4\right)^{2}=-\frac{3}{4}$$

Multiply both sides by -12.

$$\frac{-\frac{1}{12}\left(x-4\right)^{2}}{-\frac{1}{12}}=-\frac{\frac{3}{4}}{-\frac{1}{12}}$$

Dividing by -\frac{1}{12} undoes the multiplication by -\frac{1}{12}.

$$\left(x-4\right)^{2}=-\frac{\frac{3}{4}}{-\frac{1}{12}}$$

Divide -\frac{3}{4} by -\frac{1}{12} by multiplying -\frac{3}{4} by the reciprocal of -\frac{1}{12}.

$$\left(x-4\right)^{2}=9$$

Take the square root of both sides of the equation.

$$x-4=3 x-4=-3$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=3-\left(-4\right) x-4-\left(-4\right)=-3-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=3-\left(-4\right) x=-3-\left(-4\right)$$

Subtract -4 from 3.

$$x=7$$

Subtract -4 from -3.

$$x=1$$

The equation is now solved.

$$x=7 x=1$$