Solve (x+1)^2=-25(y-1)

$$( x + 1 ) ^ { 2 } = - 25 ( y - 1 )$$

Solve for y

$$y=-\frac{\left(x-4\right)\left(x+6\right)}{25}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

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

Use the distributive property to multiply -25 by y-1.

$$x^{2}+2x+1=-25y+25$$

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

$$-25y+25=x^{2}+2x+1$$

Subtract 25 from both sides.

$$-25y=x^{2}+2x+1-25$$

Subtract 25 from 1 to get -24.

$$-25y=x^{2}+2x-24$$

Divide both sides by -25.

$$\frac{-25y}{-25}=\frac{\left(x-4\right)\left(x+6\right)}{-25}$$

Dividing by -25 undoes the multiplication by -25.

$$y=\frac{\left(x-4\right)\left(x+6\right)}{-25}$$

Divide \left(-4+x\right)\left(6+x\right) by -25.

$$y=-\frac{\left(x-4\right)\left(x+6\right)}{25}$$

Solve for x (complex solution)

$$x=-5\sqrt{1-y}-1$$

$$x=5\sqrt{1-y}-1$$

Solve for x

$$x=-5\sqrt{1-y}-1$$

$$x=5\sqrt{1-y}-1\text{, }y\leq 1$$