Solve 27m^2+49=0

$$27 m ^ { 2 } + 49 = 0$$

Solve for m

$$m=-\frac{7\sqrt{3}i}{9}\approx -0-1.347150628i$$

$$m=\frac{7\sqrt{3}i}{9}\approx 1.347150628i$$

Steps by Finding Square Root

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

$$27m^{2}=-49$$

Divide both sides by 27.

$$m^{2}=-\frac{49}{27}$$

The equation is now solved.

$$m=\frac{7\sqrt{3}i}{9} m=-\frac{7\sqrt{3}i}{9}$$

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.

$$27m^{2}+49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 27 for a, 0 for b, and 49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 27\times 49}}{2\times 27}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 27\times 49}}{2\times 27}$$

Multiply -4 times 27.

$$m=\frac{0±\sqrt{-108\times 49}}{2\times 27}$$

Multiply -108 times 49.

$$m=\frac{0±\sqrt{-5292}}{2\times 27}$$

Take the square root of -5292.

$$m=\frac{0±42\sqrt{3}i}{2\times 27}$$

Multiply 2 times 27.

$$m=\frac{0±42\sqrt{3}i}{54}$$

Now solve the equation m=\frac{0±42\sqrt{3}i}{54} when ± is plus.

$$m=\frac{7\sqrt{3}i}{9}$$

Now solve the equation m=\frac{0±42\sqrt{3}i}{54} when ± is minus.

$$m=-\frac{7\sqrt{3}i}{9}$$

The equation is now solved.

$$m=\frac{7\sqrt{3}i}{9} m=-\frac{7\sqrt{3}i}{9}$$