Solve 49b^2-1=0

$$49 b ^ { 2 } - 1 = 0$$

Solve for b

$$b=\frac{1}{7}\approx 0.142857143$$

$$b=-\frac{1}{7}\approx -0.142857143$$

Steps Using Difference of Squares

Consider 49b^{2}-1. Rewrite 49b^{2}-1 as \left(7b\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7b-1\right)\left(7b+1\right)=0$$

To find equation solutions, solve 7b-1=0 and 7b+1=0.

$$b=\frac{1}{7} b=-\frac{1}{7}$$

Steps by Finding Square Root

Add 1 to both sides. Anything plus zero gives itself.

$$49b^{2}=1$$

Divide both sides by 49.

$$b^{2}=\frac{1}{49}$$

Take the square root of both sides of the equation.

$$b=\frac{1}{7} b=-\frac{1}{7}$$

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.

$$49b^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 49\left(-1\right)}}{2\times 49}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 49\left(-1\right)}}{2\times 49}$$

Multiply -4 times 49.

$$b=\frac{0±\sqrt{-196\left(-1\right)}}{2\times 49}$$

Multiply -196 times -1.

$$b=\frac{0±\sqrt{196}}{2\times 49}$$

Take the square root of 196.

$$b=\frac{0±14}{2\times 49}$$

Multiply 2 times 49.

$$b=\frac{0±14}{98}$$

Now solve the equation b=\frac{0±14}{98} when ± is plus. Reduce the fraction \frac{14}{98} to lowest terms by extracting and canceling out 14.

$$b=\frac{1}{7}$$

Now solve the equation b=\frac{0±14}{98} when ± is minus. Reduce the fraction \frac{-14}{98} to lowest terms by extracting and canceling out 14.

$$b=-\frac{1}{7}$$

The equation is now solved.

$$b=\frac{1}{7} b=-\frac{1}{7}$$