Solve x-(25%x-(40%)x)(10%x)=45

$$x - ( 25 \% x - ( 40 \% ) x ) ( 10 \% x ) = 45$$

Solve for x

$$x = \frac{10 \sqrt{370} - 100}{3} \approx 30.784613539$$

$$x=\frac{-10\sqrt{370}-100}{3}\approx -97.451280206$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$x-\left(\frac{1}{4}x-\frac{40}{100}x\right)\times \frac{10}{100}x=45$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$x-\left(\frac{1}{4}x-\frac{2}{5}x\right)\times \frac{10}{100}x=45$$

Combine \frac{1}{4}x and -\frac{2}{5}x to get -\frac{3}{20}x.

$$x-\left(-\frac{3}{20}x\times \frac{10}{100}x\right)=45$$

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

$$x-\left(-\frac{3}{20}x\times \frac{1}{10}x\right)=45$$

Multiply -\frac{3}{20} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$x-\frac{-3}{20\times 10}xx=45$$

Do the multiplications in the fraction \frac{-3}{20\times 10}.

$$x-\frac{-3}{200}xx=45$$

Fraction \frac{-3}{200} can be rewritten as -\frac{3}{200} by extracting the negative sign.

$$x-\left(-\frac{3}{200}xx\right)=45$$

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

$$x-\left(-\frac{3}{200}x^{2}\right)=45$$

The opposite of -\frac{3}{200}x^{2} is \frac{3}{200}x^{2}.

$$x+\frac{3}{200}x^{2}=45$$

Subtract 45 from both sides.

$$x+\frac{3}{200}x^{2}-45=0$$

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.

$$\frac{3}{200}x^{2}+x-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{200} for a, 1 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times \frac{3}{200}\left(-45\right)}}{2\times \frac{3}{200}}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\times \frac{3}{200}\left(-45\right)}}{2\times \frac{3}{200}}$$

Multiply -4 times \frac{3}{200}.

$$x=\frac{-1±\sqrt{1-\frac{3}{50}\left(-45\right)}}{2\times \frac{3}{200}}$$

Multiply -\frac{3}{50} times -45.

$$x=\frac{-1±\sqrt{1+\frac{27}{10}}}{2\times \frac{3}{200}}$$

Add 1 to \frac{27}{10}.

$$x=\frac{-1±\sqrt{\frac{37}{10}}}{2\times \frac{3}{200}}$$

Take the square root of \frac{37}{10}.

$$x=\frac{-1±\frac{\sqrt{370}}{10}}{2\times \frac{3}{200}}$$

Multiply 2 times \frac{3}{200}.

$$x=\frac{-1±\frac{\sqrt{370}}{10}}{\frac{3}{100}}$$

Now solve the equation x=\frac{-1±\frac{\sqrt{370}}{10}}{\frac{3}{100}} when ± is plus. Add -1 to \frac{\sqrt{370}}{10}.

$$x=\frac{\frac{\sqrt{370}}{10}-1}{\frac{3}{100}}$$

Divide -1+\frac{\sqrt{370}}{10} by \frac{3}{100} by multiplying -1+\frac{\sqrt{370}}{10} by the reciprocal of \frac{3}{100}.

$$x=\frac{10\sqrt{370}-100}{3}$$

Now solve the equation x=\frac{-1±\frac{\sqrt{370}}{10}}{\frac{3}{100}} when ± is minus. Subtract \frac{\sqrt{370}}{10} from -1.

$$x=\frac{-\frac{\sqrt{370}}{10}-1}{\frac{3}{100}}$$

Divide -1-\frac{\sqrt{370}}{10} by \frac{3}{100} by multiplying -1-\frac{\sqrt{370}}{10} by the reciprocal of \frac{3}{100}.

$$x=\frac{-10\sqrt{370}-100}{3}$$

The equation is now solved.

$$x=\frac{10\sqrt{370}-100}{3} x=\frac{-10\sqrt{370}-100}{3}$$

Steps for Completing the Square

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$x-\left(\frac{1}{4}x-\frac{40}{100}x\right)\times \frac{10}{100}x=45$$

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$x-\left(\frac{1}{4}x-\frac{2}{5}x\right)\times \frac{10}{100}x=45$$

Combine \frac{1}{4}x and -\frac{2}{5}x to get -\frac{3}{20}x.

$$x-\left(-\frac{3}{20}x\times \frac{10}{100}x\right)=45$$

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

$$x-\left(-\frac{3}{20}x\times \frac{1}{10}x\right)=45$$

Multiply -\frac{3}{20} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$x-\frac{-3}{20\times 10}xx=45$$

Do the multiplications in the fraction \frac{-3}{20\times 10}.

$$x-\frac{-3}{200}xx=45$$

Fraction \frac{-3}{200} can be rewritten as -\frac{3}{200} by extracting the negative sign.

$$x-\left(-\frac{3}{200}xx\right)=45$$

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

$$x-\left(-\frac{3}{200}x^{2}\right)=45$$

The opposite of -\frac{3}{200}x^{2} is \frac{3}{200}x^{2}.

$$x+\frac{3}{200}x^{2}=45$$

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.

$$\frac{3}{200}x^{2}+x=45$$

Divide both sides of the equation by \frac{3}{200}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{200}x^{2}+x}{\frac{3}{200}}=\frac{45}{\frac{3}{200}}$$

Dividing by \frac{3}{200} undoes the multiplication by \frac{3}{200}.

$$x^{2}+\frac{1}{\frac{3}{200}}x=\frac{45}{\frac{3}{200}}$$

Divide 1 by \frac{3}{200} by multiplying 1 by the reciprocal of \frac{3}{200}.

$$x^{2}+\frac{200}{3}x=\frac{45}{\frac{3}{200}}$$

Divide 45 by \frac{3}{200} by multiplying 45 by the reciprocal of \frac{3}{200}.

$$x^{2}+\frac{200}{3}x=3000$$

Divide \frac{200}{3}, the coefficient of the x term, by 2 to get \frac{100}{3}. Then add the square of \frac{100}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{200}{3}x+\left(\frac{100}{3}\right)^{2}=3000+\left(\frac{100}{3}\right)^{2}$$

Square \frac{100}{3} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{200}{3}x+\frac{10000}{9}=3000+\frac{10000}{9}$$

Add 3000 to \frac{10000}{9}.

$$x^{2}+\frac{200}{3}x+\frac{10000}{9}=\frac{37000}{9}$$

Factor x^{2}+\frac{200}{3}x+\frac{10000}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{100}{3}\right)^{2}=\frac{37000}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{100}{3}\right)^{2}}=\sqrt{\frac{37000}{9}}$$

Simplify.

$$x+\frac{100}{3}=\frac{10\sqrt{370}}{3} x+\frac{100}{3}=-\frac{10\sqrt{370}}{3}$$

Subtract \frac{100}{3} from both sides of the equation.

$$x=\frac{10\sqrt{370}-100}{3} x=\frac{-10\sqrt{370}-100}{3}$$