Solve 11q^2-44=0

$$11 q ^ { 2 } - 44 = 0$$

Solve for q

$$q=2$$

$$q=-2$$

Steps Using Difference of Squares

Divide both sides by 11.

$$q^{2}-4=0$$

Consider q^{2}-4. Rewrite q^{2}-4 as q^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(q-2\right)\left(q+2\right)=0$$

To find equation solutions, solve q-2=0 and q+2=0.

$$q=2 q=-2$$

Steps by Finding Square Root

Add 44 to both sides. Anything plus zero gives itself.

$$11q^{2}=44$$

Divide both sides by 11.

$$q^{2}=\frac{44}{11}$$

Divide 44 by 11 to get 4.

$$q^{2}=4$$

Take the square root of both sides of the equation.

$$q=2 q=-2$$

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.

$$11q^{2}-44=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -44 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\times 11\left(-44\right)}}{2\times 11}$$

Square 0.

$$q=\frac{0±\sqrt{-4\times 11\left(-44\right)}}{2\times 11}$$

Multiply -4 times 11.

$$q=\frac{0±\sqrt{-44\left(-44\right)}}{2\times 11}$$

Multiply -44 times -44.

$$q=\frac{0±\sqrt{1936}}{2\times 11}$$

Take the square root of 1936.

$$q=\frac{0±44}{2\times 11}$$

Multiply 2 times 11.

$$q=\frac{0±44}{22}$$

Now solve the equation q=\frac{0±44}{22} when ± is plus. Divide 44 by 22.

$$q=2$$

Now solve the equation q=\frac{0±44}{22} when ± is minus. Divide -44 by 22.

$$q=-2$$

The equation is now solved.

$$q=2 q=-2$$