Solve (z)^2*3/16=36/3

$$\frac { ( z ) ^ { 2 } \times 3 } { 16 } = \frac { 36 } { 3 }$$

Solve for z

$$z=8$$

$$z=-8$$

Steps Using Difference of Squares

Multiply both sides of the equation by 48, the least common multiple of 16,3.

$$3z^{2}\times 3=16\times 36$$

Multiply 3 and 3 to get 9.

$$9z^{2}=16\times 36$$

Multiply 16 and 36 to get 576.

$$9z^{2}=576$$

Subtract 576 from both sides.

$$9z^{2}-576=0$$

Divide both sides by 9.

$$z^{2}-64=0$$

Consider z^{2}-64. Rewrite z^{2}-64 as z^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-8\right)\left(z+8\right)=0$$

To find equation solutions, solve z-8=0 and z+8=0.

$$z=8 z=-8$$

Steps by Finding Square Root

Multiply both sides of the equation by 48, the least common multiple of 16,3.

$$3z^{2}\times 3=16\times 36$$

Multiply 3 and 3 to get 9.

$$9z^{2}=16\times 36$$

Multiply 16 and 36 to get 576.

$$9z^{2}=576$$

Divide both sides by 9.

$$z^{2}=\frac{576}{9}$$

Divide 576 by 9 to get 64.

$$z^{2}=64$$

Take the square root of both sides of the equation.

$$z=8 z=-8$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 48, the least common multiple of 16,3.

$$3z^{2}\times 3=16\times 36$$

Multiply 3 and 3 to get 9.

$$9z^{2}=16\times 36$$

Multiply 16 and 36 to get 576.

$$9z^{2}=576$$

Subtract 576 from both sides.

$$9z^{2}-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 9\left(-576\right)}}{2\times 9}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 9\left(-576\right)}}{2\times 9}$$

Multiply -4 times 9.

$$z=\frac{0±\sqrt{-36\left(-576\right)}}{2\times 9}$$

Multiply -36 times -576.

$$z=\frac{0±\sqrt{20736}}{2\times 9}$$

Take the square root of 20736.

$$z=\frac{0±144}{2\times 9}$$

Multiply 2 times 9.

$$z=\frac{0±144}{18}$$

Now solve the equation z=\frac{0±144}{18} when ± is plus. Divide 144 by 18.

$$z=8$$

Now solve the equation z=\frac{0±144}{18} when ± is minus. Divide -144 by 18.

$$z=-8$$

The equation is now solved.

$$z=8 z=-8$$