Solve 4n^2-100=0

$$4 n ^ { 2 } - 100 = 0$$

Solve for n

$$n=5$$

$$n=-5$$

Steps Using Difference of Squares

Divide both sides by 4.

$$n^{2}-25=0$$

Consider n^{2}-25. Rewrite n^{2}-25 as n^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-5\right)\left(n+5\right)=0$$

To find equation solutions, solve n-5=0 and n+5=0.

$$n=5 n=-5$$

Steps by Finding Square Root

Add 100 to both sides. Anything plus zero gives itself.

$$4n^{2}=100$$

Divide both sides by 4.

$$n^{2}=\frac{100}{4}$$

Divide 100 by 4 to get 25.

$$n^{2}=25$$

Take the square root of both sides of the equation.

$$n=5 n=-5$$

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.

$$4n^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 4\left(-100\right)}}{2\times 4}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 4\left(-100\right)}}{2\times 4}$$

Multiply -4 times 4.

$$n=\frac{0±\sqrt{-16\left(-100\right)}}{2\times 4}$$

Multiply -16 times -100.

$$n=\frac{0±\sqrt{1600}}{2\times 4}$$

Take the square root of 1600.

$$n=\frac{0±40}{2\times 4}$$

Multiply 2 times 4.

$$n=\frac{0±40}{8}$$

Now solve the equation n=\frac{0±40}{8} when ± is plus. Divide 40 by 8.

$$n=5$$

Now solve the equation n=\frac{0±40}{8} when ± is minus. Divide -40 by 8.

$$n=-5$$

The equation is now solved.

$$n=5 n=-5$$