Solve z^2-2510^-12+1610^-12=0

$${ z }^{ 2 } -25 { 10 }^{ -12 } +16 { 10 }^{ -12 } =0$$

Solve for z

$$z=\frac{3}{1000000}=0.000003$$

$$z=-\frac{3}{1000000}=-0.000003$$

Steps by Finding Square Root

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$z^{2}-25\times \frac{1}{1000000000000}+16\times 10^{-12}=0$$

Multiply 25 and \frac{1}{1000000000000} to get \frac{1}{40000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times 10^{-12}=0$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times \frac{1}{1000000000000}=0$$

Multiply 16 and \frac{1}{1000000000000} to get \frac{1}{62500000000}.

$$z^{2}-\frac{1}{40000000000}+\frac{1}{62500000000}=0$$

Add -\frac{1}{40000000000} and \frac{1}{62500000000} to get -\frac{9}{1000000000000}.

$$z^{2}-\frac{9}{1000000000000}=0$$

Add \frac{9}{1000000000000} to both sides. Anything plus zero gives itself.

$$z^{2}=\frac{9}{1000000000000}$$

Take the square root of both sides of the equation.

$$z=\frac{3}{1000000} z=-\frac{3}{1000000}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$z^{2}-25\times \frac{1}{1000000000000}+16\times 10^{-12}=0$$

Multiply 25 and \frac{1}{1000000000000} to get \frac{1}{40000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times 10^{-12}=0$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times \frac{1}{1000000000000}=0$$

Multiply 16 and \frac{1}{1000000000000} to get \frac{1}{62500000000}.

$$z^{2}-\frac{1}{40000000000}+\frac{1}{62500000000}=0$$

Add -\frac{1}{40000000000} and \frac{1}{62500000000} to get -\frac{9}{1000000000000}.

$$z^{2}-\frac{9}{1000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{9}{1000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{1000000000000}\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-\frac{9}{1000000000000}\right)}}{2}$$

Multiply -4 times -\frac{9}{1000000000000}.

$$z=\frac{0±\sqrt{\frac{9}{250000000000}}}{2}$$

Take the square root of \frac{9}{250000000000}.

$$z=\frac{0±\frac{3}{500000}}{2}$$

Now solve the equation z=\frac{0±\frac{3}{500000}}{2} when ± is plus.

$$z=\frac{3}{1000000}$$

Now solve the equation z=\frac{0±\frac{3}{500000}}{2} when ± is minus.

$$z=-\frac{3}{1000000}$$

The equation is now solved.

$$z=\frac{3}{1000000} z=-\frac{3}{1000000}$$