Solve 5b^2-1=449

$$5 b ^ { 2 } - 1 = 449$$

Solve for b

$$b=3\sqrt{10}\approx 9.486832981$$

$$b=-3\sqrt{10}\approx -9.486832981$$

Steps by Finding Square Root

Add 1 to both sides.

$$5b^{2}=449+1$$

Add 449 and 1 to get 450.

$$5b^{2}=450$$

Divide both sides by 5.

$$b^{2}=\frac{450}{5}$$

Divide 450 by 5 to get 90.

$$b^{2}=90$$

Take the square root of both sides of the equation.

$$b=3\sqrt{10} b=-3\sqrt{10}$$

Steps Using the Quadratic Formula

Subtract 449 from both sides.

$$5b^{2}-1-449=0$$

Subtract 449 from -1 to get -450.

$$5b^{2}-450=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -450 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 5\left(-450\right)}}{2\times 5}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 5\left(-450\right)}}{2\times 5}$$

Multiply -4 times 5.

$$b=\frac{0±\sqrt{-20\left(-450\right)}}{2\times 5}$$

Multiply -20 times -450.

$$b=\frac{0±\sqrt{9000}}{2\times 5}$$

Take the square root of 9000.

$$b=\frac{0±30\sqrt{10}}{2\times 5}$$

Multiply 2 times 5.

$$b=\frac{0±30\sqrt{10}}{10}$$

Now solve the equation b=\frac{0±30\sqrt{10}}{10} when ± is plus.

$$b=3\sqrt{10}$$

Now solve the equation b=\frac{0±30\sqrt{10}}{10} when ± is minus.

$$b=-3\sqrt{10}$$

The equation is now solved.

$$b=3\sqrt{10} b=-3\sqrt{10}$$