Solve x-78=5(y-7)^2

$$x - 78 = 5 ( y - 7 ) ^ { 2 }$$

Solve for x

$$x=5\left(y-7\right)^{2}+78$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-7\right)^{2}.

$$x-78=5\left(y^{2}-14y+49\right)$$

Use the distributive property to multiply 5 by y^{2}-14y+49.

$$x-78=5y^{2}-70y+245$$

Add 78 to both sides.

$$x=5y^{2}-70y+245+78$$

Add 245 and 78 to get 323.

$$x=5y^{2}-70y+323$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{5x-390}}{5}+7$$

$$y=\frac{\sqrt{5x-390}}{5}+7$$

Solve for y

$$y=-\frac{\sqrt{5x-390}}{5}+7$$

$$y=\frac{\sqrt{5x-390}}{5}+7\text{, }x\geq 78$$