Solve 3140*(1+x)*0.9*(700*(1-1.3x)+210)=3140*700*(1+12.86%)

$$3140 \times (1+x) \times 0.9 \times (700 \times (1-1.3x)+210)=3140 \times 700 \times (1+12.86 \% )$$

Solve for x

$$x=\frac{\sqrt{598}}{130}\approx 0.188107989$$

$$x=-\frac{\sqrt{598}}{130}\approx -0.188107989$$

Steps by Finding Square Root

Cancel out 3140 on both sides.

$$\left(1+x\right)\times 0.9\left(700\left(1-1.3x\right)+210\right)=700\left(1+\frac{12.86}{100}\right)$$

Use the distributive property to multiply 700 by 1-1.3x.

$$\left(1+x\right)\times 0.9\left(700-910x+210\right)=700\left(1+\frac{12.86}{100}\right)$$

Add 700 and 210 to get 910.

$$\left(1+x\right)\times 0.9\left(910-910x\right)=700\left(1+\frac{12.86}{100}\right)$$

Use the distributive property to multiply 1+x by 0.9.

$$\left(0.9+0.9x\right)\left(910-910x\right)=700\left(1+\frac{12.86}{100}\right)$$

Apply the distributive property by multiplying each term of 0.9+0.9x by each term of 910-910x.

$$819-819x+819x-819x^{2}=700\left(1+\frac{12.86}{100}\right)$$

Combine -819x and 819x to get 0.

$$819-819x^{2}=700\left(1+\frac{12.86}{100}\right)$$

Expand \frac{12.86}{100} by multiplying both numerator and the denominator by 100.

$$819-819x^{2}=700\left(1+\frac{1286}{10000}\right)$$

Reduce the fraction \frac{1286}{10000} to lowest terms by extracting and canceling out 2.

$$819-819x^{2}=700\left(1+\frac{643}{5000}\right)$$

Convert 1 to fraction \frac{5000}{5000}.

$$819-819x^{2}=700\left(\frac{5000}{5000}+\frac{643}{5000}\right)$$

Since \frac{5000}{5000} and \frac{643}{5000} have the same denominator, add them by adding their numerators.

$$819-819x^{2}=700\times \frac{5000+643}{5000}$$

Add 5000 and 643 to get 5643.

$$819-819x^{2}=700\times \frac{5643}{5000}$$

Express 700\times \frac{5643}{5000} as a single fraction.

$$819-819x^{2}=\frac{700\times 5643}{5000}$$

Multiply 700 and 5643 to get 3950100.

$$819-819x^{2}=\frac{3950100}{5000}$$

Reduce the fraction \frac{3950100}{5000} to lowest terms by extracting and canceling out 100.

$$819-819x^{2}=\frac{39501}{50}$$

Subtract 819 from both sides.

$$-819x^{2}=\frac{39501}{50}-819$$

Convert 819 to fraction \frac{40950}{50}.

$$-819x^{2}=\frac{39501}{50}-\frac{40950}{50}$$

Since \frac{39501}{50} and \frac{40950}{50} have the same denominator, subtract them by subtracting their numerators.

$$-819x^{2}=\frac{39501-40950}{50}$$

Subtract 40950 from 39501 to get -1449.

$$-819x^{2}=-\frac{1449}{50}$$

Divide both sides by -819.

$$x^{2}=\frac{-\frac{1449}{50}}{-819}$$

Express \frac{-\frac{1449}{50}}{-819} as a single fraction.

$$x^{2}=\frac{-1449}{50\left(-819\right)}$$

Multiply 50 and -819 to get -40950.

$$x^{2}=\frac{-1449}{-40950}$$

Reduce the fraction \frac{-1449}{-40950} to lowest terms by extracting and canceling out -63.

$$x^{2}=\frac{23}{650}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{598}}{130} x=-\frac{\sqrt{598}}{130}$$

Steps Using the Quadratic Formula

Cancel out 3140 on both sides.

$$\left(1+x\right)\times 0.9\left(700\left(1-1.3x\right)+210\right)=700\left(1+\frac{12.86}{100}\right)$$

Use the distributive property to multiply 700 by 1-1.3x.

$$\left(1+x\right)\times 0.9\left(700-910x+210\right)=700\left(1+\frac{12.86}{100}\right)$$

Add 700 and 210 to get 910.

$$\left(1+x\right)\times 0.9\left(910-910x\right)=700\left(1+\frac{12.86}{100}\right)$$

Use the distributive property to multiply 1+x by 0.9.

$$\left(0.9+0.9x\right)\left(910-910x\right)=700\left(1+\frac{12.86}{100}\right)$$

Apply the distributive property by multiplying each term of 0.9+0.9x by each term of 910-910x.

$$819-819x+819x-819x^{2}=700\left(1+\frac{12.86}{100}\right)$$

Combine -819x and 819x to get 0.

$$819-819x^{2}=700\left(1+\frac{12.86}{100}\right)$$

Expand \frac{12.86}{100} by multiplying both numerator and the denominator by 100.

$$819-819x^{2}=700\left(1+\frac{1286}{10000}\right)$$

Reduce the fraction \frac{1286}{10000} to lowest terms by extracting and canceling out 2.

$$819-819x^{2}=700\left(1+\frac{643}{5000}\right)$$

Convert 1 to fraction \frac{5000}{5000}.

$$819-819x^{2}=700\left(\frac{5000}{5000}+\frac{643}{5000}\right)$$

Since \frac{5000}{5000} and \frac{643}{5000} have the same denominator, add them by adding their numerators.

$$819-819x^{2}=700\times \frac{5000+643}{5000}$$

Add 5000 and 643 to get 5643.

$$819-819x^{2}=700\times \frac{5643}{5000}$$

Express 700\times \frac{5643}{5000} as a single fraction.

$$819-819x^{2}=\frac{700\times 5643}{5000}$$

Multiply 700 and 5643 to get 3950100.

$$819-819x^{2}=\frac{3950100}{5000}$$

Reduce the fraction \frac{3950100}{5000} to lowest terms by extracting and canceling out 100.

$$819-819x^{2}=\frac{39501}{50}$$

Subtract \frac{39501}{50} from both sides.

$$819-819x^{2}-\frac{39501}{50}=0$$

Convert 819 to fraction \frac{40950}{50}.

$$\frac{40950}{50}-819x^{2}-\frac{39501}{50}=0$$

Since \frac{40950}{50} and \frac{39501}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40950-39501}{50}-819x^{2}=0$$

Subtract 39501 from 40950 to get 1449.

$$\frac{1449}{50}-819x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-819x^{2}+\frac{1449}{50}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -819 for a, 0 for b, and \frac{1449}{50} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-819\right)\times \frac{1449}{50}}}{2\left(-819\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-819\right)\times \frac{1449}{50}}}{2\left(-819\right)}$$

Multiply -4 times -819.

$$x=\frac{0±\sqrt{3276\times \frac{1449}{50}}}{2\left(-819\right)}$$

Multiply 3276 times \frac{1449}{50}.

$$x=\frac{0±\sqrt{\frac{2373462}{25}}}{2\left(-819\right)}$$

Take the square root of \frac{2373462}{25}.

$$x=\frac{0±\frac{63\sqrt{598}}{5}}{2\left(-819\right)}$$

Multiply 2 times -819.

$$x=\frac{0±\frac{63\sqrt{598}}{5}}{-1638}$$

Now solve the equation x=\frac{0±\frac{63\sqrt{598}}{5}}{-1638} when ± is plus.

$$x=-\frac{\sqrt{598}}{130}$$

Now solve the equation x=\frac{0±\frac{63\sqrt{598}}{5}}{-1638} when ± is minus.

$$x=\frac{\sqrt{598}}{130}$$

The equation is now solved.

$$x=-\frac{\sqrt{598}}{130} x=\frac{\sqrt{598}}{130}$$