Solve 2z^2=50

$$2 z ^ { 2 } = 50$$

Solve for z

$$z=5$$

$$z=-5$$

Steps Using Difference of Squares

Divide both sides by 2.

$$z^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$z^{2}=25$$

Subtract 25 from both sides.

$$z^{2}-25=0$$

Consider z^{2}-25. Rewrite z^{2}-25 as z^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-5\right)\left(z+5\right)=0$$

To find equation solutions, solve z-5=0 and z+5=0.

$$z=5 z=-5$$

Steps by Finding Square Root

Divide both sides by 2.

$$z^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$z^{2}=25$$

Take the square root of both sides of the equation.

$$z=5 z=-5$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$z^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$z^{2}=25$$

Subtract 25 from both sides.

$$z^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-25\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-25\right)}}{2}$$

Multiply -4 times -25.

$$z=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$z=\frac{0±10}{2}$$

Now solve the equation z=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$z=5$$

Now solve the equation z=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$z=-5$$

The equation is now solved.

$$z=5 z=-5$$