Solve 41/4.9=x^2

$$\frac { 41 } { 4.9 } = x ^ { 2 }$$

Solve for x

$$x = \frac{\sqrt{410}}{7} \approx 2.892636676$$

$$x = -\frac{\sqrt{410}}{7} \approx -2.892636676$$

Steps by Finding Square Root

Expand \frac{41}{4.9} by multiplying both numerator and the denominator by 10.

$$\frac{410}{49}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{410}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{410}}{7} x=-\frac{\sqrt{410}}{7}$$

Steps Using the Quadratic Formula

Expand \frac{41}{4.9} by multiplying both numerator and the denominator by 10.

$$\frac{410}{49}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{410}{49}$$

Subtract \frac{410}{49} from both sides.

$$x^{2}-\frac{410}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{410}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{410}{49}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{410}{49}\right)}}{2}$$

Multiply -4 times -\frac{410}{49}.

$$x=\frac{0±\sqrt{\frac{1640}{49}}}{2}$$

Take the square root of \frac{1640}{49}.

$$x=\frac{0±\frac{2\sqrt{410}}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{410}}{7}}{2} when ± is plus.

$$x=\frac{\sqrt{410}}{7}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{410}}{7}}{2} when ± is minus.

$$x=-\frac{\sqrt{410}}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{410}}{7} x=-\frac{\sqrt{410}}{7}$$