Solve 50x^2+45+500-85=80%

$$50 { x }^{ 2 } +45+500-85=80 \%$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{1435}i}{25}\approx -0-3.030511508i$$

$$x=\frac{2\sqrt{1435}i}{25}\approx 3.030511508i$$

Steps by Finding Square Root

Add 45 and 500 to get 545.

$$50x^{2}+545-85=\frac{80}{100}$$

Subtract 85 from 545 to get 460.

$$50x^{2}+460=\frac{80}{100}$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$50x^{2}+460=\frac{4}{5}$$

Subtract 460 from both sides.

$$50x^{2}=\frac{4}{5}-460$$

Subtract 460 from \frac{4}{5} to get -\frac{2296}{5}.

$$50x^{2}=-\frac{2296}{5}$$

Divide both sides by 50.

$$x^{2}=\frac{-\frac{2296}{5}}{50}$$

Express \frac{-\frac{2296}{5}}{50} as a single fraction.

$$x^{2}=\frac{-2296}{5\times 50}$$

Multiply 5 and 50 to get 250.

$$x^{2}=\frac{-2296}{250}$$

Reduce the fraction \frac{-2296}{250} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{1148}{125}$$

The equation is now solved.

$$x=\frac{2\sqrt{1435}i}{25} x=-\frac{2\sqrt{1435}i}{25}$$

Steps Using the Quadratic Formula

Add 45 and 500 to get 545.

$$50x^{2}+545-85=\frac{80}{100}$$

Subtract 85 from 545 to get 460.

$$50x^{2}+460=\frac{80}{100}$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$50x^{2}+460=\frac{4}{5}$$

Subtract \frac{4}{5} from both sides.

$$50x^{2}+460-\frac{4}{5}=0$$

Subtract \frac{4}{5} from 460 to get \frac{2296}{5}.

$$50x^{2}+\frac{2296}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 50 for a, 0 for b, and \frac{2296}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 50\times \frac{2296}{5}}}{2\times 50}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 50\times \frac{2296}{5}}}{2\times 50}$$

Multiply -4 times 50.

$$x=\frac{0±\sqrt{-200\times \frac{2296}{5}}}{2\times 50}$$

Multiply -200 times \frac{2296}{5}.

$$x=\frac{0±\sqrt{-91840}}{2\times 50}$$

Take the square root of -91840.

$$x=\frac{0±8\sqrt{1435}i}{2\times 50}$$

Multiply 2 times 50.

$$x=\frac{0±8\sqrt{1435}i}{100}$$

Now solve the equation x=\frac{0±8\sqrt{1435}i}{100} when ± is plus.

$$x=\frac{2\sqrt{1435}i}{25}$$

Now solve the equation x=\frac{0±8\sqrt{1435}i}{100} when ± is minus.

$$x=-\frac{2\sqrt{1435}i}{25}$$

The equation is now solved.

$$x=\frac{2\sqrt{1435}i}{25} x=-\frac{2\sqrt{1435}i}{25}$$