Solve 2y^2-50=0

$$2 y ^ { 2 } - 50 = 0$$

Solve for y

$$y=5$$

$$y=-5$$

Steps Using Difference of Squares

Divide both sides by 2.

$$y^{2}-25=0$$

Consider y^{2}-25. Rewrite y^{2}-25 as y^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-5\right)\left(y+5\right)=0$$

To find equation solutions, solve y-5=0 and y+5=0.

$$y=5 y=-5$$

Steps by Finding Square Root

Add 50 to both sides. Anything plus zero gives itself.

$$2y^{2}=50$$

Divide both sides by 2.

$$y^{2}=\frac{50}{2}$$

Divide 50 by 2 to get 25.

$$y^{2}=25$$

Take the square root of both sides of the equation.

$$y=5 y=-5$$

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.

$$2y^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 2\left(-50\right)}}{2\times 2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 2\left(-50\right)}}{2\times 2}$$

Multiply -4 times 2.

$$y=\frac{0±\sqrt{-8\left(-50\right)}}{2\times 2}$$

Multiply -8 times -50.

$$y=\frac{0±\sqrt{400}}{2\times 2}$$

Take the square root of 400.

$$y=\frac{0±20}{2\times 2}$$

Multiply 2 times 2.

$$y=\frac{0±20}{4}$$

Now solve the equation y=\frac{0±20}{4} when ± is plus. Divide 20 by 4.

$$y=5$$

Now solve the equation y=\frac{0±20}{4} when ± is minus. Divide -20 by 4.

$$y=-5$$

The equation is now solved.

$$y=5 y=-5$$