Solve (a-1)(a+1)=36

$$( a - 1 ) ( a + 1 ) = 36$$

Solve for a

$$a=\sqrt{37}\approx 6.08276253$$

$$a=-\sqrt{37}\approx -6.08276253$$

Steps by Finding Square Root

Consider \left(a-1\right)\left(a+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$a^{2}-1=36$$

Add 1 to both sides.

$$a^{2}=36+1$$

Add 36 and 1 to get 37.

$$a^{2}=37$$

Take the square root of both sides of the equation.

$$a=\sqrt{37} a=-\sqrt{37}$$

Steps Using the Quadratic Formula

Consider \left(a-1\right)\left(a+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$a^{2}-1=36$$

Subtract 36 from both sides.

$$a^{2}-1-36=0$$

Subtract 36 from -1 to get -37.

$$a^{2}-37=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -37 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-37\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-37\right)}}{2}$$

Multiply -4 times -37.

$$a=\frac{0±\sqrt{148}}{2}$$

Take the square root of 148.

$$a=\frac{0±2\sqrt{37}}{2}$$

Now solve the equation a=\frac{0±2\sqrt{37}}{2} when ± is plus.

$$a=\sqrt{37}$$

Now solve the equation a=\frac{0±2\sqrt{37}}{2} when ± is minus.

$$a=-\sqrt{37}$$

The equation is now solved.

$$a=\sqrt{37} a=-\sqrt{37}$$