Solve 5z^2-10=0

$$5 z ^ { 2 } - 10 = 0$$

Solve for z

$$z=\sqrt{2}\approx 1.414213562$$

$$z=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Add 10 to both sides. Anything plus zero gives itself.

$$5z^{2}=10$$

Divide both sides by 5.

$$z^{2}=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$z^{2}=2$$

Take the square root of both sides of the equation.

$$z=\sqrt{2} z=-\sqrt{2}$$

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.

$$5z^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\times 5\left(-10\right)}}{2\times 5}$$

Square 0.

$$z=\frac{0±\sqrt{-4\times 5\left(-10\right)}}{2\times 5}$$

Multiply -4 times 5.

$$z=\frac{0±\sqrt{-20\left(-10\right)}}{2\times 5}$$

Multiply -20 times -10.

$$z=\frac{0±\sqrt{200}}{2\times 5}$$

Take the square root of 200.

$$z=\frac{0±10\sqrt{2}}{2\times 5}$$

Multiply 2 times 5.

$$z=\frac{0±10\sqrt{2}}{10}$$

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

$$z=\sqrt{2}$$

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

$$z=-\sqrt{2}$$

The equation is now solved.

$$z=\sqrt{2} z=-\sqrt{2}$$