Solve 196x^2=256

$$196 x ^ { 2 } = 256$$

Solve for x

$$x = \frac{8}{7} = 1\frac{1}{7} \approx 1.142857143$$

$$x = -\frac{8}{7} = -1\frac{1}{7} \approx -1.142857143$$

Steps Using Difference of Squares

Divide both sides by 196.

$$x^{2}=\frac{256}{196}$$

Reduce the fraction \frac{256}{196} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{64}{49}$$

Subtract \frac{64}{49} from both sides.

$$x^{2}-\frac{64}{49}=0$$

Multiply both sides by 49.

$$49x^{2}-64=0$$

Consider 49x^{2}-64. Rewrite 49x^{2}-64 as \left(7x\right)^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(7x-8\right)\left(7x+8\right)=0$$

To find equation solutions, solve 7x-8=0 and 7x+8=0.

$$x=\frac{8}{7} x=-\frac{8}{7}$$

Steps by Finding Square Root

Divide both sides by 196.

$$x^{2}=\frac{256}{196}$$

Reduce the fraction \frac{256}{196} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{64}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{8}{7} x=-\frac{8}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 196.

$$x^{2}=\frac{256}{196}$$

Reduce the fraction \frac{256}{196} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{64}{49}$$

Subtract \frac{64}{49} from both sides.

$$x^{2}-\frac{64}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{64}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{64}{49}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{64}{49}\right)}}{2}$$

Multiply -4 times -\frac{64}{49}.

$$x=\frac{0±\sqrt{\frac{256}{49}}}{2}$$

Take the square root of \frac{256}{49}.

$$x=\frac{0±\frac{16}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{16}{7}}{2} when ± is plus.

$$x=\frac{8}{7}$$

Now solve the equation x=\frac{0±\frac{16}{7}}{2} when ± is minus.

$$x=-\frac{8}{7}$$

The equation is now solved.

$$x=\frac{8}{7} x=-\frac{8}{7}$$