Solve x^2=308*7div22*8

$${ x }^{ 2 } =308 \times 7 \div 22 \times 8$$

Solve for x

$$x=28$$

$$x=-28$$

Steps Using Difference of Squares

Multiply both sides of the equation by 22.

$$22x^{2}=308\times 7\times 8$$

Multiply 308 and 7 to get 2156.

$$22x^{2}=2156\times 8$$

Multiply 2156 and 8 to get 17248.

$$22x^{2}=17248$$

Subtract 17248 from both sides.

$$22x^{2}-17248=0$$

Divide both sides by 22.

$$x^{2}-784=0$$

Consider x^{2}-784. Rewrite x^{2}-784 as x^{2}-28^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-28\right)\left(x+28\right)=0$$

To find equation solutions, solve x-28=0 and x+28=0.

$$x=28 x=-28$$

Steps by Finding Square Root

Multiply both sides of the equation by 22.

$$22x^{2}=308\times 7\times 8$$

Multiply 308 and 7 to get 2156.

$$22x^{2}=2156\times 8$$

Multiply 2156 and 8 to get 17248.

$$22x^{2}=17248$$

Divide both sides by 22.

$$x^{2}=\frac{17248}{22}$$

Divide 17248 by 22 to get 784.

$$x^{2}=784$$

Take the square root of both sides of the equation.

$$x=28 x=-28$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 22.

$$22x^{2}=308\times 7\times 8$$

Multiply 308 and 7 to get 2156.

$$22x^{2}=2156\times 8$$

Multiply 2156 and 8 to get 17248.

$$22x^{2}=17248$$

Subtract 17248 from both sides.

$$22x^{2}-17248=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 22 for a, 0 for b, and -17248 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 22\left(-17248\right)}}{2\times 22}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 22\left(-17248\right)}}{2\times 22}$$

Multiply -4 times 22.

$$x=\frac{0±\sqrt{-88\left(-17248\right)}}{2\times 22}$$

Multiply -88 times -17248.

$$x=\frac{0±\sqrt{1517824}}{2\times 22}$$

Take the square root of 1517824.

$$x=\frac{0±1232}{2\times 22}$$

Multiply 2 times 22.

$$x=\frac{0±1232}{44}$$

Now solve the equation x=\frac{0±1232}{44} when ± is plus. Divide 1232 by 44.

$$x=28$$

Now solve the equation x=\frac{0±1232}{44} when ± is minus. Divide -1232 by 44.

$$x=-28$$

The equation is now solved.

$$x=28 x=-28$$