Solve 91n^2+49=0

$$91 n ^ { 2 } + 49 = 0$$

Solve for n

$$n=-\frac{\sqrt{91}i}{13}\approx -0-0.733799386i$$

$$n=\frac{\sqrt{91}i}{13}\approx 0.733799386i$$

Steps by Finding Square Root

Subtract 49 from both sides. Anything subtracted from zero gives its negation.

$$91n^{2}=-49$$

Divide both sides by 91.

$$n^{2}=\frac{-49}{91}$$

Reduce the fraction \frac{-49}{91} to lowest terms by extracting and canceling out 7.

$$n^{2}=-\frac{7}{13}$$

The equation is now solved.

$$n=\frac{\sqrt{91}i}{13} n=-\frac{\sqrt{91}i}{13}$$

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.

$$91n^{2}+49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 91 for a, 0 for b, and 49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 91\times 49}}{2\times 91}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 91\times 49}}{2\times 91}$$

Multiply -4 times 91.

$$n=\frac{0±\sqrt{-364\times 49}}{2\times 91}$$

Multiply -364 times 49.

$$n=\frac{0±\sqrt{-17836}}{2\times 91}$$

Take the square root of -17836.

$$n=\frac{0±14\sqrt{91}i}{2\times 91}$$

Multiply 2 times 91.

$$n=\frac{0±14\sqrt{91}i}{182}$$

Now solve the equation n=\frac{0±14\sqrt{91}i}{182} when ± is plus.

$$n=\frac{\sqrt{91}i}{13}$$

Now solve the equation n=\frac{0±14\sqrt{91}i}{182} when ± is minus.

$$n=-\frac{\sqrt{91}i}{13}$$

The equation is now solved.

$$n=\frac{\sqrt{91}i}{13} n=-\frac{\sqrt{91}i}{13}$$