Solve -y^2+5=0

$$- y ^ { 2 } + 5 = 0$$

Solve for y

$$y=\sqrt{5}\approx 2.236067977$$

$$y=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-y^{2}=-5$$

Divide both sides by -1.

$$y^{2}=\frac{-5}{-1}$$

Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.

$$y^{2}=5$$

Take the square root of both sides of the equation.

$$y=\sqrt{5} y=-\sqrt{5}$$

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.

$$-y^{2}+5=0$$

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

$$y=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$y=\frac{0±\sqrt{4\times 5}}{2\left(-1\right)}$$

Multiply 4 times 5.

$$y=\frac{0±\sqrt{20}}{2\left(-1\right)}$$

Take the square root of 20.

$$y=\frac{0±2\sqrt{5}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$y=\frac{0±2\sqrt{5}}{-2}$$

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

$$y=-\sqrt{5}$$

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

$$y=\sqrt{5}$$

The equation is now solved.

$$y=-\sqrt{5} y=\sqrt{5}$$