Solve 1/2quada^2=1/29

$$\frac { 1 } { 2 } \quad a ^ { 2 } = \frac { 1 } { 29 }$$

Solve for a

$$a=\frac{\sqrt{58}}{29}\approx 0.262612866$$

$$a=-\frac{\sqrt{58}}{29}\approx -0.262612866$$

Steps by Finding Square Root

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$a^{2}=\frac{1}{29}\times 2$$

Multiply \frac{1}{29} and 2 to get \frac{2}{29}.

$$a^{2}=\frac{2}{29}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{58}}{29} a=-\frac{\sqrt{58}}{29}$$

Steps Using the Quadratic Formula

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$a^{2}=\frac{1}{29}\times 2$$

Multiply \frac{1}{29} and 2 to get \frac{2}{29}.

$$a^{2}=\frac{2}{29}$$

Subtract \frac{2}{29} from both sides.

$$a^{2}-\frac{2}{29}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{2}{29} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{2}{29}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{2}{29}\right)}}{2}$$

Multiply -4 times -\frac{2}{29}.

$$a=\frac{0±\sqrt{\frac{8}{29}}}{2}$$

Take the square root of \frac{8}{29}.

$$a=\frac{0±\frac{2\sqrt{58}}{29}}{2}$$

Now solve the equation a=\frac{0±\frac{2\sqrt{58}}{29}}{2} when ± is plus.

$$a=\frac{\sqrt{58}}{29}$$

Now solve the equation a=\frac{0±\frac{2\sqrt{58}}{29}}{2} when ± is minus.

$$a=-\frac{\sqrt{58}}{29}$$

The equation is now solved.

$$a=\frac{\sqrt{58}}{29} a=-\frac{\sqrt{58}}{29}$$