Solve x^2-1=pi

$$x ^ { 2 } - 1 = \pi$$

Solve for x

$$x=\sqrt{\pi +1}\approx 2.035090331$$

$$x=-\sqrt{\pi +1}\approx -2.035090331$$

Steps by Finding Square Root

Add 1 to both sides of the equation.

$$x^{2}-1+1=\pi +1$$

Subtracting 1 from itself leaves 0.

$$x^{2}=\pi +1$$

Take the square root of both sides of the equation.

$$x=\sqrt{\pi +1} x=-\sqrt{\pi +1}$$

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.

$$x^{2}-1=\pi$$

Subtract \pi from both sides of the equation.

$$x^{2}-1-\pi =\pi -\pi$$

Subtracting \pi from itself leaves 0.

$$x^{2}-1-\pi =0$$

Subtract \pi from -1.

$$x^{2}-\pi -1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-\pi -1\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\pi -1\right)}}{2}$$

Multiply -4 times -1-\pi .

$$x=\frac{0±\sqrt{4\pi +4}}{2}$$

Take the square root of 4+4\pi .

$$x=\frac{0±2\sqrt{\pi +1}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{\pi +1}}{2} when ± is plus.

$$x=\sqrt{\pi +1}$$

Now solve the equation x=\frac{0±2\sqrt{\pi +1}}{2} when ± is minus.

$$x=-\sqrt{\pi +1}$$

The equation is now solved.

$$x=\sqrt{\pi +1} x=-\sqrt{\pi +1}$$