Solve 2z^2=98

$$2 z ^ { 2 } = 98$$

Solve for z

$$z=7$$

$$z=-7$$

Steps Using Difference of Squares

Divide both sides by 2.

$$z^{2}=\frac{98}{2}$$

Divide 98 by 2 to get 49.

$$z^{2}=49$$

Subtract 49 from both sides.

$$z^{2}-49=0$$

Consider z^{2}-49. Rewrite z^{2}-49 as z^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(z-7\right)\left(z+7\right)=0$$

To find equation solutions, solve z-7=0 and z+7=0.

$$z=7 z=-7$$

Steps by Finding Square Root

Divide both sides by 2.

$$z^{2}=\frac{98}{2}$$

Divide 98 by 2 to get 49.

$$z^{2}=49$$

Take the square root of both sides of the equation.

$$z=7 z=-7$$

Steps Using the Quadratic Formula

Divide both sides by 2.

$$z^{2}=\frac{98}{2}$$

Divide 98 by 2 to get 49.

$$z^{2}=49$$

Subtract 49 from both sides.

$$z^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-49\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-49\right)}}{2}$$

Multiply -4 times -49.

$$z=\frac{0±\sqrt{196}}{2}$$

Take the square root of 196.

$$z=\frac{0±14}{2}$$

Now solve the equation z=\frac{0±14}{2} when ± is plus. Divide 14 by 2.

$$z=7$$

Now solve the equation z=\frac{0±14}{2} when ± is minus. Divide -14 by 2.

$$z=-7$$

The equation is now solved.

$$z=7 z=-7$$