Solve z*5z=5

$$z \times 5z=5$$

Solve for z

$$z=1$$

$$z=-1$$

Steps by Finding Square Root

Multiply z and z to get z^{2}.

$$z^{2}\times 5=5$$

Divide both sides by 5.

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

Divide 5 by 5 to get 1.

$$z^{2}=1$$

Take the square root of both sides of the equation.

$$z=1 z=-1$$

Steps Using the Quadratic Formula

Multiply z and z to get z^{2}.

$$z^{2}\times 5=5$$

Subtract 5 from both sides.

$$z^{2}\times 5-5=0$$

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.

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

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

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

Square 0.

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

Multiply -4 times 5.

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

Multiply -20 times -5.

$$z=\frac{0±\sqrt{100}}{2\times 5}$$

Take the square root of 100.

$$z=\frac{0±10}{2\times 5}$$

Multiply 2 times 5.

$$z=\frac{0±10}{10}$$

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

$$z=1$$

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

$$z=-1$$

The equation is now solved.

$$z=1 z=-1$$