Solve {l}{{(90f)}{(x)}=12x^2+48x+60}{9{(x)}=2x+3}{g=f{(x)}}{text{Solvefor}htext{where}}{h=g}

$$\left. \begin{array} { l } { {(90 f)} {(x)} = 12 x ^ {2} + 48 x + 60 }\\ { 9 {(x)} = 2 x + 3 }\\ { g = f {(x)} }\\ { \text{Solve for } h \text{ where} } \\ { h = g } \end{array} \right.$$

Solve for f, x, g, h

$$h=\frac{676}{735}\approx 0.919727891$$

Solution Steps

Consider the second equation. Subtract 2x from both sides.

$$9x-2x=3$$

Combine 9x and -2x to get 7x.

$$7x=3$$

Divide both sides by 7.

$$x=\frac{3}{7}$$

Consider the first equation. Insert the known values of variables into the equation.

$$90f\times \frac{3}{7}=12\times \left(\frac{3}{7}\right)^{2}+48\times \frac{3}{7}+60$$

Multiply 90 and \frac{3}{7} to get \frac{270}{7}.

$$\frac{270}{7}f=12\times \left(\frac{3}{7}\right)^{2}+48\times \frac{3}{7}+60$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{270}{7}f=12\times \frac{9}{49}+48\times \frac{3}{7}+60$$

Multiply 12 and \frac{9}{49} to get \frac{108}{49}.

$$\frac{270}{7}f=\frac{108}{49}+48\times \frac{3}{7}+60$$

Multiply 48 and \frac{3}{7} to get \frac{144}{7}.

$$\frac{270}{7}f=\frac{108}{49}+\frac{144}{7}+60$$

Add \frac{108}{49} and \frac{144}{7} to get \frac{1116}{49}.

$$\frac{270}{7}f=\frac{1116}{49}+60$$

Add \frac{1116}{49} and 60 to get \frac{4056}{49}.

$$\frac{270}{7}f=\frac{4056}{49}$$

Multiply both sides by \frac{7}{270}, the reciprocal of \frac{270}{7}.

$$f=\frac{4056}{49}\times \frac{7}{270}$$

Multiply \frac{4056}{49} and \frac{7}{270} to get \frac{676}{315}.

$$f=\frac{676}{315}$$

Consider the third equation. Insert the known values of variables into the equation.

$$g=\frac{676}{315}\times \frac{3}{7}$$

Multiply \frac{676}{315} and \frac{3}{7} to get \frac{676}{735}.

$$g=\frac{676}{735}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$h=\frac{676}{735}$$

The system is now solved.

$$f=\frac{676}{315} x=\frac{3}{7} g=\frac{676}{735} h=\frac{676}{735}$$