Solve 111y^2-10y^2-243=98y^2

$$111 y ^ { 2 } - 10 y ^ { 2 } - 243 = 98 y ^ { 2 }$$

Solve for y

$$y=9$$

$$y=-9$$

Steps Using Difference of Squares

Combine 111y^{2} and -10y^{2} to get 101y^{2}.

$$101y^{2}-243=98y^{2}$$

Subtract 98y^{2} from both sides.

$$101y^{2}-243-98y^{2}=0$$

Combine 101y^{2} and -98y^{2} to get 3y^{2}.

$$3y^{2}-243=0$$

Divide both sides by 3.

$$y^{2}-81=0$$

Consider y^{2}-81. Rewrite y^{2}-81 as y^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(y-9\right)\left(y+9\right)=0$$

To find equation solutions, solve y-9=0 and y+9=0.

$$y=9 y=-9$$

Steps by Finding Square Root

Combine 111y^{2} and -10y^{2} to get 101y^{2}.

$$101y^{2}-243=98y^{2}$$

Subtract 98y^{2} from both sides.

$$101y^{2}-243-98y^{2}=0$$

Combine 101y^{2} and -98y^{2} to get 3y^{2}.

$$3y^{2}-243=0$$

Add 243 to both sides. Anything plus zero gives itself.

$$3y^{2}=243$$

Divide both sides by 3.

$$y^{2}=\frac{243}{3}$$

Divide 243 by 3 to get 81.

$$y^{2}=81$$

Take the square root of both sides of the equation.

$$y=9 y=-9$$

Steps Using the Quadratic Formula

Combine 111y^{2} and -10y^{2} to get 101y^{2}.

$$101y^{2}-243=98y^{2}$$

Subtract 98y^{2} from both sides.

$$101y^{2}-243-98y^{2}=0$$

Combine 101y^{2} and -98y^{2} to get 3y^{2}.

$$3y^{2}-243=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -243 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 3\left(-243\right)}}{2\times 3}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 3\left(-243\right)}}{2\times 3}$$

Multiply -4 times 3.

$$y=\frac{0±\sqrt{-12\left(-243\right)}}{2\times 3}$$

Multiply -12 times -243.

$$y=\frac{0±\sqrt{2916}}{2\times 3}$$

Take the square root of 2916.

$$y=\frac{0±54}{2\times 3}$$

Multiply 2 times 3.

$$y=\frac{0±54}{6}$$

Now solve the equation y=\frac{0±54}{6} when ± is plus. Divide 54 by 6.

$$y=9$$

Now solve the equation y=\frac{0±54}{6} when ± is minus. Divide -54 by 6.

$$y=-9$$

The equation is now solved.

$$y=9 y=-9$$