Solve a^2+16a^2=1

$$a ^ { 2 } + 16 a ^ { 2 } = 1$$

Solve for a

$$a=\frac{\sqrt{17}}{17}\approx 0.242535625$$

$$a=-\frac{\sqrt{17}}{17}\approx -0.242535625$$

Steps by Finding Square Root

Combine a^{2} and 16a^{2} to get 17a^{2}.

$$17a^{2}=1$$

Divide both sides by 17.

$$a^{2}=\frac{1}{17}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{17}}{17} a=-\frac{\sqrt{17}}{17}$$

Steps Using the Quadratic Formula

Combine a^{2} and 16a^{2} to get 17a^{2}.

$$17a^{2}=1$$

Subtract 1 from both sides.

$$17a^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 17 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 17\left(-1\right)}}{2\times 17}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 17\left(-1\right)}}{2\times 17}$$

Multiply -4 times 17.

$$a=\frac{0±\sqrt{-68\left(-1\right)}}{2\times 17}$$

Multiply -68 times -1.

$$a=\frac{0±\sqrt{68}}{2\times 17}$$

Take the square root of 68.

$$a=\frac{0±2\sqrt{17}}{2\times 17}$$

Multiply 2 times 17.

$$a=\frac{0±2\sqrt{17}}{34}$$

Now solve the equation a=\frac{0±2\sqrt{17}}{34} when ± is plus.

$$a=\frac{\sqrt{17}}{17}$$

Now solve the equation a=\frac{0±2\sqrt{17}}{34} when ± is minus.

$$a=-\frac{\sqrt{17}}{17}$$

The equation is now solved.

$$a=\frac{\sqrt{17}}{17} a=-\frac{\sqrt{17}}{17}$$