Solve x-10/100*-5/100*(x-10/100x)=342

$$\frac { x - 10 } { 100 } \times \frac { - 5 } { 100 } \cdot ( x - \frac { 10 } { 100 } x ) = 342$$

Solve for x (complex solution)

$$x=5+5\sqrt{30399}i\approx 5+871.765450107i$$

$$x=-5\sqrt{30399}i+5\approx 5-871.765450107i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 100.

$$\left(x-10\right)\times \frac{-5}{100}\left(x-\frac{10}{100}x\right)=34200$$

Reduce the fraction \frac{-5}{100} to lowest terms by extracting and canceling out 5.

$$\left(x-10\right)\left(-\frac{1}{20}\right)\left(x-\frac{10}{100}x\right)=34200$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$\left(x-10\right)\left(-\frac{1}{20}\right)\left(x-\frac{1}{10}x\right)=34200$$

Combine x and -\frac{1}{10}x to get \frac{9}{10}x.

$$\left(x-10\right)\left(-\frac{1}{20}\right)\times \frac{9}{10}x=34200$$

Multiply -\frac{1}{20} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\left(x-10\right)\times \frac{-9}{20\times 10}x=34200$$

Do the multiplications in the fraction \frac{-9}{20\times 10}.

$$\left(x-10\right)\times \frac{-9}{200}x=34200$$

Fraction \frac{-9}{200} can be rewritten as -\frac{9}{200} by extracting the negative sign.

$$\left(x-10\right)\left(-\frac{9}{200}\right)x=34200$$

Use the distributive property to multiply x-10 by -\frac{9}{200}.

$$\left(x\left(-\frac{9}{200}\right)-10\left(-\frac{9}{200}\right)\right)x=34200$$

Express -10\left(-\frac{9}{200}\right) as a single fraction.

$$\left(x\left(-\frac{9}{200}\right)+\frac{-10\left(-9\right)}{200}\right)x=34200$$

Multiply -10 and -9 to get 90.

$$\left(x\left(-\frac{9}{200}\right)+\frac{90}{200}\right)x=34200$$

Reduce the fraction \frac{90}{200} to lowest terms by extracting and canceling out 10.

$$\left(x\left(-\frac{9}{200}\right)+\frac{9}{20}\right)x=34200$$

Use the distributive property to multiply x\left(-\frac{9}{200}\right)+\frac{9}{20} by x.

$$x\left(-\frac{9}{200}\right)x+\frac{9}{20}x=34200$$

Multiply x and x to get x^{2}.

$$x^{2}\left(-\frac{9}{200}\right)+\frac{9}{20}x=34200$$

Subtract 34200 from both sides.

$$x^{2}\left(-\frac{9}{200}\right)+\frac{9}{20}x-34200=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-\frac{9}{200}x^{2}+\frac{9}{20}x-34200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{9}{200} for a, \frac{9}{20} for b, and -34200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{9}{20}±\sqrt{\left(\frac{9}{20}\right)^{2}-4\left(-\frac{9}{200}\right)\left(-34200\right)}}{2\left(-\frac{9}{200}\right)}$$

Square \frac{9}{20} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{9}{20}±\sqrt{\frac{81}{400}-4\left(-\frac{9}{200}\right)\left(-34200\right)}}{2\left(-\frac{9}{200}\right)}$$

Multiply -4 times -\frac{9}{200}.

$$x=\frac{-\frac{9}{20}±\sqrt{\frac{81}{400}+\frac{9}{50}\left(-34200\right)}}{2\left(-\frac{9}{200}\right)}$$

Multiply \frac{9}{50} times -34200.

$$x=\frac{-\frac{9}{20}±\sqrt{\frac{81}{400}-6156}}{2\left(-\frac{9}{200}\right)}$$

Add \frac{81}{400} to -6156.

$$x=\frac{-\frac{9}{20}±\sqrt{-\frac{2462319}{400}}}{2\left(-\frac{9}{200}\right)}$$

Take the square root of -\frac{2462319}{400}.

$$x=\frac{-\frac{9}{20}±\frac{9\sqrt{30399}i}{20}}{2\left(-\frac{9}{200}\right)}$$

Multiply 2 times -\frac{9}{200}.

$$x=\frac{-\frac{9}{20}±\frac{9\sqrt{30399}i}{20}}{-\frac{9}{100}}$$

Now solve the equation x=\frac{-\frac{9}{20}±\frac{9\sqrt{30399}i}{20}}{-\frac{9}{100}} when ± is plus. Add -\frac{9}{20} to \frac{9i\sqrt{30399}}{20}.

$$x=\frac{-9+9\sqrt{30399}i}{-\frac{9}{100}\times 20}$$

Divide \frac{-9+9i\sqrt{30399}}{20} by -\frac{9}{100} by multiplying \frac{-9+9i\sqrt{30399}}{20} by the reciprocal of -\frac{9}{100}.

$$x=-5\sqrt{30399}i+5$$

Now solve the equation x=\frac{-\frac{9}{20}±\frac{9\sqrt{30399}i}{20}}{-\frac{9}{100}} when ± is minus. Subtract \frac{9i\sqrt{30399}}{20} from -\frac{9}{20}.

$$x=\frac{-9\sqrt{30399}i-9}{-\frac{9}{100}\times 20}$$

Divide \frac{-9-9i\sqrt{30399}}{20} by -\frac{9}{100} by multiplying \frac{-9-9i\sqrt{30399}}{20} by the reciprocal of -\frac{9}{100}.

$$x=5+5\sqrt{30399}i$$

The equation is now solved.

$$x=-5\sqrt{30399}i+5 x=5+5\sqrt{30399}i$$

Steps for Completing the Square

Multiply both sides of the equation by 100.

$$\left(x-10\right)\times \frac{-5}{100}\left(x-\frac{10}{100}x\right)=34200$$

Reduce the fraction \frac{-5}{100} to lowest terms by extracting and canceling out 5.

$$\left(x-10\right)\left(-\frac{1}{20}\right)\left(x-\frac{10}{100}x\right)=34200$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$\left(x-10\right)\left(-\frac{1}{20}\right)\left(x-\frac{1}{10}x\right)=34200$$

Combine x and -\frac{1}{10}x to get \frac{9}{10}x.

$$\left(x-10\right)\left(-\frac{1}{20}\right)\times \frac{9}{10}x=34200$$

Multiply -\frac{1}{20} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\left(x-10\right)\times \frac{-9}{20\times 10}x=34200$$

Do the multiplications in the fraction \frac{-9}{20\times 10}.

$$\left(x-10\right)\times \frac{-9}{200}x=34200$$

Fraction \frac{-9}{200} can be rewritten as -\frac{9}{200} by extracting the negative sign.

$$\left(x-10\right)\left(-\frac{9}{200}\right)x=34200$$

Use the distributive property to multiply x-10 by -\frac{9}{200}.

$$\left(x\left(-\frac{9}{200}\right)-10\left(-\frac{9}{200}\right)\right)x=34200$$

Express -10\left(-\frac{9}{200}\right) as a single fraction.

$$\left(x\left(-\frac{9}{200}\right)+\frac{-10\left(-9\right)}{200}\right)x=34200$$

Multiply -10 and -9 to get 90.

$$\left(x\left(-\frac{9}{200}\right)+\frac{90}{200}\right)x=34200$$

Reduce the fraction \frac{90}{200} to lowest terms by extracting and canceling out 10.

$$\left(x\left(-\frac{9}{200}\right)+\frac{9}{20}\right)x=34200$$

Use the distributive property to multiply x\left(-\frac{9}{200}\right)+\frac{9}{20} by x.

$$x\left(-\frac{9}{200}\right)x+\frac{9}{20}x=34200$$

Multiply x and x to get x^{2}.

$$x^{2}\left(-\frac{9}{200}\right)+\frac{9}{20}x=34200$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-\frac{9}{200}x^{2}+\frac{9}{20}x=34200$$

Divide both sides of the equation by -\frac{9}{200}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{9}{200}x^{2}+\frac{9}{20}x}{-\frac{9}{200}}=\frac{34200}{-\frac{9}{200}}$$

Dividing by -\frac{9}{200} undoes the multiplication by -\frac{9}{200}.

$$x^{2}+\frac{\frac{9}{20}}{-\frac{9}{200}}x=\frac{34200}{-\frac{9}{200}}$$

Divide \frac{9}{20} by -\frac{9}{200} by multiplying \frac{9}{20} by the reciprocal of -\frac{9}{200}.

$$x^{2}-10x=\frac{34200}{-\frac{9}{200}}$$

Divide 34200 by -\frac{9}{200} by multiplying 34200 by the reciprocal of -\frac{9}{200}.

$$x^{2}-10x=-760000$$

Divide -10, the coefficient of the x term, by 2 to get -5. Then add the square of -5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-10x+\left(-5\right)^{2}=-760000+\left(-5\right)^{2}$$

Square -5.

$$x^{2}-10x+25=-760000+25$$

Add -760000 to 25.

$$x^{2}-10x+25=-759975$$

Factor x^{2}-10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-5\right)^{2}=-759975$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{-759975}$$

Simplify.

$$x-5=5\sqrt{30399}i x-5=-5\sqrt{30399}i$$

Add 5 to both sides of the equation.

$$x=5+5\sqrt{30399}i x=-5\sqrt{30399}i+5$$