Solve (x^2+1)*5=43

$$( x ^ { 2 } + 1 ) \cdot 5 = 43$$

Solve for x

$$x = \frac{\sqrt{190}}{5} \approx 2.75680975$$

$$x = -\frac{\sqrt{190}}{5} \approx -2.75680975$$

Steps by Finding Square Root

Divide both sides by 5.

$$x^{2}+1=\frac{43}{5}$$

Subtract 1 from both sides.

$$x^{2}=\frac{43}{5}-1$$

Subtract 1 from \frac{43}{5} to get \frac{38}{5}.

$$x^{2}=\frac{38}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{190}}{5} x=-\frac{\sqrt{190}}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$x^{2}+1=\frac{43}{5}$$

Subtract \frac{43}{5} from both sides.

$$x^{2}+1-\frac{43}{5}=0$$

Subtract \frac{43}{5} from 1 to get -\frac{38}{5}.

$$x^{2}-\frac{38}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{38}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{38}{5}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{38}{5}\right)}}{2}$$

Multiply -4 times -\frac{38}{5}.

$$x=\frac{0±\sqrt{\frac{152}{5}}}{2}$$

Take the square root of \frac{152}{5}.

$$x=\frac{0±\frac{2\sqrt{190}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{190}}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{190}}{5}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{190}}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{190}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{190}}{5} x=-\frac{\sqrt{190}}{5}$$