Solve 41-x^2=0

$$41 - x ^ { 2 } = 0$$

Solve for x

$$x=\sqrt{41}\approx 6.403124237$$

$$x=-\sqrt{41}\approx -6.403124237$$

Steps by Finding Square Root

Subtract 41 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-41$$

Divide both sides by -1.

$$x^{2}=\frac{-41}{-1}$$

Fraction \frac{-41}{-1} can be simplified to 41 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=41$$

Take the square root of both sides of the equation.

$$x=\sqrt{41} x=-\sqrt{41}$$

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.

$$-x^{2}+41=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 41 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 41}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 41}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 41}}{2\left(-1\right)}$$

Multiply 4 times 41.

$$x=\frac{0±\sqrt{164}}{2\left(-1\right)}$$

Take the square root of 164.

$$x=\frac{0±2\sqrt{41}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{41}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{41}}{-2} when ± is plus.

$$x=-\sqrt{41}$$

Now solve the equation x=\frac{0±2\sqrt{41}}{-2} when ± is minus.

$$x=\sqrt{41}$$

The equation is now solved.

$$x=-\sqrt{41} x=\sqrt{41}$$