Solve 9/10^2+4/b^2=1

$$\frac { 9 } { 10 ^ { 2 } } + \frac { 4 } { b ^ { 2 } } = 1$$

Solve for b

$$b = \frac{20 \sqrt{91}}{91} \approx 2.096569673$$

$$b = -\frac{20 \sqrt{91}}{91} \approx -2.096569673$$

Steps by Finding Square Root

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}.

$$\frac{1}{100}b^{2}\times 9+4=b^{2}$$

Multiply \frac{1}{100} and 9 to get \frac{9}{100}.

$$\frac{9}{100}b^{2}+4=b^{2}$$

Subtract b^{2} from both sides.

$$\frac{9}{100}b^{2}+4-b^{2}=0$$

Combine \frac{9}{100}b^{2} and -b^{2} to get -\frac{91}{100}b^{2}.

$$-\frac{91}{100}b^{2}+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{91}{100}b^{2}=-4$$

Multiply both sides by -\frac{100}{91}, the reciprocal of -\frac{91}{100}.

$$b^{2}=-4\left(-\frac{100}{91}\right)$$

Multiply -4 and -\frac{100}{91} to get \frac{400}{91}.

$$b^{2}=\frac{400}{91}$$

Take the square root of both sides of the equation.

$$b=\frac{20\sqrt{91}}{91} b=-\frac{20\sqrt{91}}{91}$$

Steps Using the Quadratic Formula

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b^{2}.

$$\frac{1}{100}b^{2}\times 9+4=b^{2}$$

Multiply \frac{1}{100} and 9 to get \frac{9}{100}.

$$\frac{9}{100}b^{2}+4=b^{2}$$

Subtract b^{2} from both sides.

$$\frac{9}{100}b^{2}+4-b^{2}=0$$

Combine \frac{9}{100}b^{2} and -b^{2} to get -\frac{91}{100}b^{2}.

$$-\frac{91}{100}b^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{91}{100} for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-\frac{91}{100}\right)\times 4}}{2\left(-\frac{91}{100}\right)}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-\frac{91}{100}\right)\times 4}}{2\left(-\frac{91}{100}\right)}$$

Multiply -4 times -\frac{91}{100}.

$$b=\frac{0±\sqrt{\frac{91}{25}\times 4}}{2\left(-\frac{91}{100}\right)}$$

Multiply \frac{91}{25} times 4.

$$b=\frac{0±\sqrt{\frac{364}{25}}}{2\left(-\frac{91}{100}\right)}$$

Take the square root of \frac{364}{25}.

$$b=\frac{0±\frac{2\sqrt{91}}{5}}{2\left(-\frac{91}{100}\right)}$$

Multiply 2 times -\frac{91}{100}.

$$b=\frac{0±\frac{2\sqrt{91}}{5}}{-\frac{91}{50}}$$

Now solve the equation b=\frac{0±\frac{2\sqrt{91}}{5}}{-\frac{91}{50}} when ± is plus.

$$b=-\frac{20\sqrt{91}}{91}$$

Now solve the equation b=\frac{0±\frac{2\sqrt{91}}{5}}{-\frac{91}{50}} when ± is minus.

$$b=\frac{20\sqrt{91}}{91}$$

The equation is now solved.

$$b=-\frac{20\sqrt{91}}{91} b=\frac{20\sqrt{91}}{91}$$