Solve 100=F+F1.618+F2.618

$$100 = F+F1.618+F2.618$$

Solve for F

$$F=-\frac{309F_{1}}{500}-\frac{309F_{2}}{500}+100$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$F+F_{1}\times 0.618+F_{2}\times 0.618=100$$

Subtract F_{1}\times 0.618 from both sides.

$$F+F_{2}\times 0.618=100-F_{1}\times 0.618$$

Subtract F_{2}\times 0.618 from both sides.

$$F=100-F_{1}\times 0.618-F_{2}\times 0.618$$

Multiply -1 and 0.618 to get -0.618.

$$F=100-0.618F_{1}-F_{2}\times 0.618$$

Multiply -1 and 0.618 to get -0.618.

$$F=100-0.618F_{1}-0.618F_{2}$$

Solve for F_1

$$F_{1}=-\frac{500F}{309}-F_{2}+\frac{50000}{309}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$F+F_{1}\times 0.618+F_{2}\times 0.618=100$$

Subtract F from both sides.

$$F_{1}\times 0.618+F_{2}\times 0.618=100-F$$

Subtract F_{2}\times 0.618 from both sides.

$$F_{1}\times 0.618=100-F-F_{2}\times 0.618$$

Multiply -1 and 0.618 to get -0.618.

$$F_{1}\times 0.618=100-F-0.618F_{2}$$

The equation is in standard form.

$$0.618F_{1}=-\frac{309F_{2}}{500}-F+100$$

Divide both sides of the equation by 0.618, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.618F_{1}}{0.618}=\frac{-\frac{309F_{2}}{500}-F+100}{0.618}$$

Dividing by 0.618 undoes the multiplication by 0.618.

$$F_{1}=\frac{-\frac{309F_{2}}{500}-F+100}{0.618}$$

Divide 100-F-\frac{309F_{2}}{500} by 0.618 by multiplying 100-F-\frac{309F_{2}}{500} by the reciprocal of 0.618.

$$F_{1}=-\frac{500F}{309}-F_{2}+\frac{50000}{309}$$