Solve (x-25/4)=-1/25*{left(-y/2right)}^2

$$(x- \frac{ 25 }{ 4 } )=- \frac{ 1 }{ 25 } \times { \left(- \frac{ y }{ 2 } \right) }^{ 2 }$$

Solve for x

$$x=-\frac{y^{2}}{100}+\frac{25}{4}$$

Short Solution Steps

Calculate -\frac{y}{2} to the power of 2 and get \left(\frac{y}{2}\right)^{2}.

$$x-\frac{25}{4}=-\frac{1}{25}\times \left(\frac{y}{2}\right)^{2}$$

To raise \frac{y}{2} to a power, raise both numerator and denominator to the power and then divide.

$$x-\frac{25}{4}=-\frac{1}{25}\times \frac{y^{2}}{2^{2}}$$

Multiply -\frac{1}{25} times \frac{y^{2}}{2^{2}} by multiplying numerator times numerator and denominator times denominator.

$$x-\frac{25}{4}=\frac{-y^{2}}{25\times 2^{2}}$$

Add \frac{25}{4} to both sides.

$$x=\frac{-y^{2}}{25\times 2^{2}}+\frac{25}{4}$$

Calculate 2 to the power of 2 and get 4.

$$x=\frac{-y^{2}}{25\times 4}+\frac{25}{4}$$

Multiply 25 and 4 to get 100.

$$x=\frac{-y^{2}}{100}+\frac{25}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 100 and 4 is 100. Multiply \frac{25}{4} times \frac{25}{25}.

$$x=\frac{-y^{2}}{100}+\frac{25\times 25}{100}$$

Since \frac{-y^{2}}{100} and \frac{25\times 25}{100} have the same denominator, add them by adding their numerators.

$$x=\frac{-y^{2}+25\times 25}{100}$$

Do the multiplications in -y^{2}+25\times 25.

$$x=\frac{-y^{2}+625}{100}$$

Divide each term of -y^{2}+625 by 100 to get -\frac{1}{100}y^{2}+\frac{25}{4}.

$$x=-\frac{1}{100}y^{2}+\frac{25}{4}$$

Solve for y (complex solution)

$$y=-5\sqrt{25-4x}$$

$$y=5\sqrt{25-4x}$$

Solve for y

$$y=5\sqrt{25-4x}$$

$$y=-5\sqrt{25-4x}\text{, }x\leq \frac{25}{4}$$