Solve x^2=2*5*10^5*0.16

$${ x }^{ 2 } =2 \times 5 \times { 10 }^{ 5 } \times 0.16$$

Solve for x

$$x=400$$

$$x=-400$$

Steps Using Difference of Squares

Multiply 2 and 5 to get 10.

$$x^{2}=10\times 10^{5}\times 0.16$$

Calculate 10 to the power of 5 and get 100000.

$$x^{2}=10\times 100000\times 0.16$$

Multiply 10 and 100000 to get 1000000.

$$x^{2}=1000000\times 0.16$$

Multiply 1000000 and 0.16 to get 160000.

$$x^{2}=160000$$

Subtract 160000 from both sides.

$$x^{2}-160000=0$$

Consider x^{2}-160000. Rewrite x^{2}-160000 as x^{2}-400^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-400\right)\left(x+400\right)=0$$

To find equation solutions, solve x-400=0 and x+400=0.

$$x=400 x=-400$$

Steps by Finding Square Root

Multiply 2 and 5 to get 10.

$$x^{2}=10\times 10^{5}\times 0.16$$

Calculate 10 to the power of 5 and get 100000.

$$x^{2}=10\times 100000\times 0.16$$

Multiply 10 and 100000 to get 1000000.

$$x^{2}=1000000\times 0.16$$

Multiply 1000000 and 0.16 to get 160000.

$$x^{2}=160000$$

Take the square root of both sides of the equation.

$$x=400 x=-400$$

Steps Using the Quadratic Formula

Multiply 2 and 5 to get 10.

$$x^{2}=10\times 10^{5}\times 0.16$$

Calculate 10 to the power of 5 and get 100000.

$$x^{2}=10\times 100000\times 0.16$$

Multiply 10 and 100000 to get 1000000.

$$x^{2}=1000000\times 0.16$$

Multiply 1000000 and 0.16 to get 160000.

$$x^{2}=160000$$

Subtract 160000 from both sides.

$$x^{2}-160000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -160000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-160000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-160000\right)}}{2}$$

Multiply -4 times -160000.

$$x=\frac{0±\sqrt{640000}}{2}$$

Take the square root of 640000.

$$x=\frac{0±800}{2}$$

Now solve the equation x=\frac{0±800}{2} when ± is plus. Divide 800 by 2.

$$x=400$$

Now solve the equation x=\frac{0±800}{2} when ± is minus. Divide -800 by 2.

$$x=-400$$

The equation is now solved.

$$x=400 x=-400$$