Solve 5-y^2=3

$$5- { y }^{ 2 } =3$$

Solve for y

$$y=\sqrt{2}\approx 1.414213562$$

$$y=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$-y^{2}=3-5$$

Subtract 5 from 3 to get -2.

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

Divide both sides by -1.

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

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$y^{2}=2$$

Take the square root of both sides of the equation.

$$y=\sqrt{2} y=-\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$5-y^{2}-3=0$$

Subtract 3 from 5 to get 2.

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

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.

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

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

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

Square 0.

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

Multiply -4 times -1.

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

Multiply 4 times 2.

$$y=\frac{0±\sqrt{8}}{2\left(-1\right)}$$

Take the square root of 8.

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

Multiply 2 times -1.

$$y=\frac{0±2\sqrt{2}}{-2}$$

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

$$y=-\sqrt{2}$$

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

$$y=\sqrt{2}$$

The equation is now solved.

$$y=-\sqrt{2} y=\sqrt{2}$$