Solve 2z^2-200=0

$$2 z ^ { 2 } - 200 = 0$$

Solve for z

$$z=10$$

$$z=-10$$

Steps Using Difference of Squares

Divide both sides by 2.

$$z^{2}-100=0$$

Consider z^{2}-100. Rewrite z^{2}-100 as z^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-10\right)\left(z+10\right)=0$$

To find equation solutions, solve z-10=0 and z+10=0.

$$z=10 z=-10$$

Steps by Finding Square Root

Add 200 to both sides. Anything plus zero gives itself.

$$2z^{2}=200$$

Divide both sides by 2.

$$z^{2}=\frac{200}{2}$$

Divide 200 by 2 to get 100.

$$z^{2}=100$$

Take the square root of both sides of the equation.

$$z=10 z=-10$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$2z^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 2\left(-200\right)}}{2\times 2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 2\left(-200\right)}}{2\times 2}$$

Multiply -4 times 2.

$$z=\frac{0±\sqrt{-8\left(-200\right)}}{2\times 2}$$

Multiply -8 times -200.

$$z=\frac{0±\sqrt{1600}}{2\times 2}$$

Take the square root of 1600.

$$z=\frac{0±40}{2\times 2}$$

Multiply 2 times 2.

$$z=\frac{0±40}{4}$$

Now solve the equation z=\frac{0±40}{4} when ± is plus. Divide 40 by 4.

$$z=10$$

Now solve the equation z=\frac{0±40}{4} when ± is minus. Divide -40 by 4.

$$z=-10$$

The equation is now solved.

$$z=10 z=-10$$