# How do you solve the equation abs(x^2-1)=3?

Apr 24, 2017

If this is a quadratic equation then $x = - 2 \mathmr{and} x = 2$

#### Explanation:

${x}^{2} - 1 = 3$

${x}^{2} - 1 - 3 = 3 - 3$

${x}^{2} - 4 = 0$

This is a quadratic equation, in which ax^2+bx+c=0.

To solve for x the equation is ${x}_{1 , \setminus : 2} = \setminus \frac{- b \setminus \pm \setminus \sqrt{{b}^{2} - 4 a c}}{2 a}$

So $x = \setminus \frac{- 0 + \setminus \sqrt{{0}^{2} - 4 \setminus \cdot \setminus 1 \setminus \left(- 4 \setminus\right)}}{2 \setminus \cdot \setminus 1} : \setminus \quad 2$

And $x = \setminus \frac{- 0 - \setminus \sqrt{{0}^{2} - 4 \setminus \cdot \setminus 1 \setminus \left(- 4 \setminus\right)}}{2 \setminus \cdot \setminus 1} : \setminus \quad - 2$

So $x = - 2 \mathmr{and} 2$

The dot means multiplication.