Solve 1000*left(1+0.06right)^-1+4000*left(1+0.06right)^-3-10000*left(1+0.06right)^-7+xleft(1+0.06right)^-8=0

$$1000 \times { \left(1+0.06 \right) }^{ -1 } +4000 \times { \left(1+0.06 \right) }^{ -3 } -10000 \times { \left(1+0.06 \right) }^{ -7 } +x { \left(1+0.06 \right) }^{ -8 } =0$$

Solve for x

$$x=3743.46743060864$$

Steps for Solving Linear Equation

Add 1 and 0.06 to get 1.06.

$$1000\times 1.06^{-1}+4000\left(1+0.06\right)^{-3}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Calculate 1.06 to the power of -1 and get \frac{50}{53}.

$$1000\times \frac{50}{53}+4000\left(1+0.06\right)^{-3}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Multiply 1000 and \frac{50}{53} to get \frac{50000}{53}.

$$\frac{50000}{53}+4000\left(1+0.06\right)^{-3}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Add 1 and 0.06 to get 1.06.

$$\frac{50000}{53}+4000\times 1.06^{-3}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Calculate 1.06 to the power of -3 and get \frac{125000}{148877}.

$$\frac{50000}{53}+4000\times \frac{125000}{148877}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Multiply 4000 and \frac{125000}{148877} to get \frac{500000000}{148877}.

$$\frac{50000}{53}+\frac{500000000}{148877}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Add \frac{50000}{53} and \frac{500000000}{148877} to get \frac{640450000}{148877}.

$$\frac{640450000}{148877}-10000\left(1+0.06\right)^{-7}+x\left(1+0.06\right)^{-8}=0$$

Add 1 and 0.06 to get 1.06.

$$\frac{640450000}{148877}-10000\times 1.06^{-7}+x\left(1+0.06\right)^{-8}=0$$

Calculate 1.06 to the power of -7 and get \frac{781250000000}{1174711139837}.

$$\frac{640450000}{148877}-10000\times \frac{781250000000}{1174711139837}+x\left(1+0.06\right)^{-8}=0$$

Multiply 10000 and \frac{781250000000}{1174711139837} to get \frac{7812500000000000}{1174711139837}.

$$\frac{640450000}{148877}-\frac{7812500000000000}{1174711139837}+x\left(1+0.06\right)^{-8}=0$$

Subtract \frac{7812500000000000}{1174711139837} from \frac{640450000}{148877} to get -\frac{2759041443550000}{1174711139837}.

$$-\frac{2759041443550000}{1174711139837}+x\left(1+0.06\right)^{-8}=0$$

Add 1 and 0.06 to get 1.06.

$$-\frac{2759041443550000}{1174711139837}+x\times 1.06^{-8}=0$$

Calculate 1.06 to the power of -8 and get \frac{39062500000000}{62259690411361}.

$$-\frac{2759041443550000}{1174711139837}+x\times \frac{39062500000000}{62259690411361}=0$$

Add \frac{2759041443550000}{1174711139837} to both sides. Anything plus zero gives itself.

$$x\times \frac{39062500000000}{62259690411361}=\frac{2759041443550000}{1174711139837}$$

Divide both sides by \frac{39062500000000}{62259690411361}.

$$x=\frac{\frac{2759041443550000}{1174711139837}}{\frac{39062500000000}{62259690411361}}$$