Solve 176=1/11x^2

$$176 = \frac { 1 } { 11 } x ^ { 2 }$$

Solve for x

$$x=44$$

$$x=-44$$

Steps Using Difference of Squares

Multiply both sides by 11, the reciprocal of \frac{1}{11}.

$$176\times 11=x^{2}$$

Multiply 176 and 11 to get 1936.

$$1936=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=1936$$

Subtract 1936 from both sides.

$$x^{2}-1936=0$$

Consider x^{2}-1936. Rewrite x^{2}-1936 as x^{2}-44^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-44\right)\left(x+44\right)=0$$

To find equation solutions, solve x-44=0 and x+44=0.

$$x=44 x=-44$$

Steps by Finding Square Root

Multiply both sides by 11, the reciprocal of \frac{1}{11}.

$$176\times 11=x^{2}$$

Multiply 176 and 11 to get 1936.

$$1936=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=1936$$

Take the square root of both sides of the equation.

$$x=44 x=-44$$

Steps Using the Quadratic Formula

Multiply both sides by 11, the reciprocal of \frac{1}{11}.

$$176\times 11=x^{2}$$

Multiply 176 and 11 to get 1936.

$$1936=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=1936$$

Subtract 1936 from both sides.

$$x^{2}-1936=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1936 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1936\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1936\right)}}{2}$$

Multiply -4 times -1936.

$$x=\frac{0±\sqrt{7744}}{2}$$

Take the square root of 7744.

$$x=\frac{0±88}{2}$$

Now solve the equation x=\frac{0±88}{2} when ± is plus. Divide 88 by 2.

$$x=44$$

Now solve the equation x=\frac{0±88}{2} when ± is minus. Divide -88 by 2.

$$x=-44$$

The equation is now solved.

$$x=44 x=-44$$