Solve y=(5x+2/7)^2

$$y = ( \frac { 5 x + 2 } { 7 } ) ^ { 2 }$$

Solve for y

$$y=\frac{\left(5x+2\right)^{2}}{49}$$

Solution Steps

To raise \frac{5x+2}{7} to a power, raise both numerator and denominator to the power and then divide.

$$y=\frac{\left(5x+2\right)^{2}}{7^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+2\right)^{2}.

$$y=\frac{25x^{2}+20x+4}{7^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$y=\frac{25x^{2}+20x+4}{49}$$

Divide each term of 25x^{2}+20x+4 by 49 to get \frac{25}{49}x^{2}+\frac{20}{49}x+\frac{4}{49}.

$$y=\frac{25}{49}x^{2}+\frac{20}{49}x+\frac{4}{49}$$

Solve for x (complex solution)

$$x=\frac{-7\sqrt{y}-2}{5}$$

$$x=\frac{7\sqrt{y}-2}{5}$$

Solve for x

$$x=\frac{-7\sqrt{y}-2}{5}$$

$$x=\frac{7\sqrt{y}-2}{5}\text{, }y\geq 0$$