Solve 1000(1+x)(098+x)=1000(1+x)+108

$$1000(1+x)(098+x)=1000(1+x)+108$$

Solve for x

$$x = \frac{\sqrt{2770}}{50} \approx 1.052615789$$

$$x = -\frac{\sqrt{2770}}{50} \approx -1.052615789$$

Steps by Finding Square Root

Multiply 0 and 98 to get 0.

$$1000\left(1+x\right)\left(0+x\right)=1000\left(1+x\right)+108$$

Anything plus zero gives itself.

$$1000\left(1+x\right)x=1000\left(1+x\right)+108$$

Use the distributive property to multiply 1000 by 1+x.

$$\left(1000+1000x\right)x=1000\left(1+x\right)+108$$

Use the distributive property to multiply 1000+1000x by x.

$$1000x+1000x^{2}=1000\left(1+x\right)+108$$

Use the distributive property to multiply 1000 by 1+x.

$$1000x+1000x^{2}=1000+1000x+108$$

Add 1000 and 108 to get 1108.

$$1000x+1000x^{2}=1108+1000x$$

Subtract 1000x from both sides.

$$1000x+1000x^{2}-1000x=1108$$

Combine 1000x and -1000x to get 0.

$$1000x^{2}=1108$$

Divide both sides by 1000.

$$x^{2}=\frac{1108}{1000}$$

Reduce the fraction \frac{1108}{1000} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{277}{250}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2770}}{50} x=-\frac{\sqrt{2770}}{50}$$

Steps Using the Quadratic Formula

Multiply 0 and 98 to get 0.

$$1000\left(1+x\right)\left(0+x\right)=1000\left(1+x\right)+108$$

Anything plus zero gives itself.

$$1000\left(1+x\right)x=1000\left(1+x\right)+108$$

Use the distributive property to multiply 1000 by 1+x.

$$\left(1000+1000x\right)x=1000\left(1+x\right)+108$$

Use the distributive property to multiply 1000+1000x by x.

$$1000x+1000x^{2}=1000\left(1+x\right)+108$$

Use the distributive property to multiply 1000 by 1+x.

$$1000x+1000x^{2}=1000+1000x+108$$

Add 1000 and 108 to get 1108.

$$1000x+1000x^{2}=1108+1000x$$

Subtract 1108 from both sides.

$$1000x+1000x^{2}-1108=1000x$$

Subtract 1000x from both sides.

$$1000x+1000x^{2}-1108-1000x=0$$

Combine 1000x and -1000x to get 0.

$$1000x^{2}-1108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1000 for a, 0 for b, and -1108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 1000\left(-1108\right)}}{2\times 1000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 1000\left(-1108\right)}}{2\times 1000}$$

Multiply -4 times 1000.

$$x=\frac{0±\sqrt{-4000\left(-1108\right)}}{2\times 1000}$$

Multiply -4000 times -1108.

$$x=\frac{0±\sqrt{4432000}}{2\times 1000}$$

Take the square root of 4432000.

$$x=\frac{0±40\sqrt{2770}}{2\times 1000}$$

Multiply 2 times 1000.

$$x=\frac{0±40\sqrt{2770}}{2000}$$

Now solve the equation x=\frac{0±40\sqrt{2770}}{2000} when ± is plus.

$$x=\frac{\sqrt{2770}}{50}$$

Now solve the equation x=\frac{0±40\sqrt{2770}}{2000} when ± is minus.

$$x=-\frac{\sqrt{2770}}{50}$$

The equation is now solved.

$$x=\frac{\sqrt{2770}}{50} x=-\frac{\sqrt{2770}}{50}$$