Solve -16v^2+121=0

$$- 16 v ^ { 2 } + 121 = 0$$

Solve for v

$$v = \frac{11}{4} = 2\frac{3}{4} = 2.75$$

$$v = -\frac{11}{4} = -2\frac{3}{4} = -2.75$$

Steps by Finding Square Root

Subtract 121 from both sides. Anything subtracted from zero gives its negation.

$$-16v^{2}=-121$$

Divide both sides by -16.

$$v^{2}=\frac{-121}{-16}$$

Fraction \frac{-121}{-16} can be simplified to \frac{121}{16} by removing the negative sign from both the numerator and the denominator.

$$v^{2}=\frac{121}{16}$$

Take the square root of both sides of the equation.

$$v=\frac{11}{4} v=-\frac{11}{4}$$

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.

$$-16v^{2}+121=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 121 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 121}}{2\left(-16\right)}$$

Square 0.

$$v=\frac{0±\sqrt{-4\left(-16\right)\times 121}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$v=\frac{0±\sqrt{64\times 121}}{2\left(-16\right)}$$

Multiply 64 times 121.

$$v=\frac{0±\sqrt{7744}}{2\left(-16\right)}$$

Take the square root of 7744.

$$v=\frac{0±88}{2\left(-16\right)}$$

Multiply 2 times -16.

$$v=\frac{0±88}{-32}$$

Now solve the equation v=\frac{0±88}{-32} when ± is plus. Reduce the fraction \frac{88}{-32} to lowest terms by extracting and canceling out 8.

$$v=-\frac{11}{4}$$

Now solve the equation v=\frac{0±88}{-32} when ± is minus. Reduce the fraction \frac{-88}{-32} to lowest terms by extracting and canceling out 8.

$$v=\frac{11}{4}$$

The equation is now solved.

$$v=-\frac{11}{4} v=\frac{11}{4}$$