Solve {l}{g{(x)}=-5x^2+25}{h=2x}{text{Solvefor}itext{where}}{i=h}

$$\left. \begin{array} { l } { g {(x)} = -5 x ^ {2} + 25 }\\ { h = 2 x }\\ { \text{Solve for } i \text{ where} } \\ { i = h } \end{array} \right.$$

Solve for g, x, h

$$x=\frac{1}{2}i=0.5i$$

$$g=-\frac{105}{2}i=-52.5i$$

$$h=i$$

Solution Steps

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

$$h=i$$

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

$$i=2x$$

Divide both sides by 2.

$$\frac{i}{2}=x$$

Divide i by 2 to get \frac{1}{2}i.

$$\frac{1}{2}i=x$$

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

$$x=\frac{1}{2}i$$

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

$$g\times \left(\frac{1}{2}i\right)=-5\times \left(\frac{1}{2}i\right)^{2}+25$$

Calculate \frac{1}{2}i to the power of 2 and get -\frac{1}{4}.

$$g\times \left(\frac{1}{2}i\right)=-5\left(-\frac{1}{4}\right)+25$$

Multiply -5 and -\frac{1}{4} to get \frac{5}{4}.

$$g\times \left(\frac{1}{2}i\right)=\frac{5}{4}+25$$

Add \frac{5}{4} and 25 to get \frac{105}{4}.

$$g\times \left(\frac{1}{2}i\right)=\frac{105}{4}$$

Divide both sides by \frac{1}{2}i.

$$g=\frac{\frac{105}{4}}{\frac{1}{2}i}$$

Multiply both numerator and denominator of \frac{\frac{105}{4}}{\frac{1}{2}i} by imaginary unit i.

$$g=\frac{\frac{105}{4}i}{-\frac{1}{2}}$$

Divide \frac{105}{4}i by -\frac{1}{2} to get -\frac{105}{2}i.

$$g=-\frac{105}{2}i$$

The system is now solved.

$$g=-\frac{105}{2}i x=\frac{1}{2}i h=i$$