Solve -7z^2+5=0

$$- 7 z ^ { 2 } + 5 = 0$$

Solve for z

$$z=\frac{\sqrt{35}}{7}\approx 0.845154255$$

$$z=-\frac{\sqrt{35}}{7}\approx -0.845154255$$

Steps by Finding Square Root

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-7z^{2}=-5$$

Divide both sides by -7.

$$z^{2}=\frac{-5}{-7}$$

Fraction \frac{-5}{-7} can be simplified to \frac{5}{7} by removing the negative sign from both the numerator and the denominator.

$$z^{2}=\frac{5}{7}$$

Take the square root of both sides of the equation.

$$z=\frac{\sqrt{35}}{7} z=-\frac{\sqrt{35}}{7}$$

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.

$$-7z^{2}+5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-7\right)\times 5}}{2\left(-7\right)}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-7\right)\times 5}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$z=\frac{0±\sqrt{28\times 5}}{2\left(-7\right)}$$

Multiply 28 times 5.

$$z=\frac{0±\sqrt{140}}{2\left(-7\right)}$$

Take the square root of 140.

$$z=\frac{0±2\sqrt{35}}{2\left(-7\right)}$$

Multiply 2 times -7.

$$z=\frac{0±2\sqrt{35}}{-14}$$

Now solve the equation z=\frac{0±2\sqrt{35}}{-14} when ± is plus.

$$z=-\frac{\sqrt{35}}{7}$$

Now solve the equation z=\frac{0±2\sqrt{35}}{-14} when ± is minus.

$$z=\frac{\sqrt{35}}{7}$$

The equation is now solved.

$$z=-\frac{\sqrt{35}}{7} z=\frac{\sqrt{35}}{7}$$