Solve x^2=107(51*14-38*4)^2/89*18*55*52

$$x ^ { 2 } = \frac { 107 ( 51 \times 14 - 38 \times 4 ) ^ { 2 } } { 89 \times 18 \times 55 \times 52 }$$

Solve for x

$$x = \frac{281 \sqrt{13617890}}{381810} \approx 2.715900981$$

$$x = -\frac{281 \sqrt{13617890}}{381810} \approx -2.715900981$$

Steps by Finding Square Root

Multiply 51 and 14 to get 714.

$$x^{2}=\frac{107\left(714-38\times 4\right)^{2}}{89\times 18\times 55\times 52}$$

Multiply 38 and 4 to get 152.

$$x^{2}=\frac{107\left(714-152\right)^{2}}{89\times 18\times 55\times 52}$$

Subtract 152 from 714 to get 562.

$$x^{2}=\frac{107\times 562^{2}}{89\times 18\times 55\times 52}$$

Calculate 562 to the power of 2 and get 315844.

$$x^{2}=\frac{107\times 315844}{89\times 18\times 55\times 52}$$

Multiply 107 and 315844 to get 33795308.

$$x^{2}=\frac{33795308}{89\times 18\times 55\times 52}$$

Multiply 89 and 18 to get 1602.

$$x^{2}=\frac{33795308}{1602\times 55\times 52}$$

Multiply 1602 and 55 to get 88110.

$$x^{2}=\frac{33795308}{88110\times 52}$$

Multiply 88110 and 52 to get 4581720.

$$x^{2}=\frac{33795308}{4581720}$$

Reduce the fraction \frac{33795308}{4581720} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{8448827}{1145430}$$

Take the square root of both sides of the equation.

$$x=\frac{281\sqrt{13617890}}{381810} x=-\frac{281\sqrt{13617890}}{381810}$$

Steps Using the Quadratic Formula

Multiply 51 and 14 to get 714.

$$x^{2}=\frac{107\left(714-38\times 4\right)^{2}}{89\times 18\times 55\times 52}$$

Multiply 38 and 4 to get 152.

$$x^{2}=\frac{107\left(714-152\right)^{2}}{89\times 18\times 55\times 52}$$

Subtract 152 from 714 to get 562.

$$x^{2}=\frac{107\times 562^{2}}{89\times 18\times 55\times 52}$$

Calculate 562 to the power of 2 and get 315844.

$$x^{2}=\frac{107\times 315844}{89\times 18\times 55\times 52}$$

Multiply 107 and 315844 to get 33795308.

$$x^{2}=\frac{33795308}{89\times 18\times 55\times 52}$$

Multiply 89 and 18 to get 1602.

$$x^{2}=\frac{33795308}{1602\times 55\times 52}$$

Multiply 1602 and 55 to get 88110.

$$x^{2}=\frac{33795308}{88110\times 52}$$

Multiply 88110 and 52 to get 4581720.

$$x^{2}=\frac{33795308}{4581720}$$

Reduce the fraction \frac{33795308}{4581720} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{8448827}{1145430}$$

Subtract \frac{8448827}{1145430} from both sides.

$$x^{2}-\frac{8448827}{1145430}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{8448827}{1145430} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{8448827}{1145430}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{8448827}{1145430}\right)}}{2}$$

Multiply -4 times -\frac{8448827}{1145430}.

$$x=\frac{0±\sqrt{\frac{16897654}{572715}}}{2}$$

Take the square root of \frac{16897654}{572715}.

$$x=\frac{0±\frac{281\sqrt{13617890}}{190905}}{2}$$

Now solve the equation x=\frac{0±\frac{281\sqrt{13617890}}{190905}}{2} when ± is plus.

$$x=\frac{281\sqrt{13617890}}{381810}$$

Now solve the equation x=\frac{0±\frac{281\sqrt{13617890}}{190905}}{2} when ± is minus.

$$x=-\frac{281\sqrt{13617890}}{381810}$$

The equation is now solved.

$$x=\frac{281\sqrt{13617890}}{381810} x=-\frac{281\sqrt{13617890}}{381810}$$