Differenciate with respect to x. Y = (x-1) √x² + 2x +2

1 Simplify  \sqrt{{x}^{2}}

x

2

​

  to  xx.

y=(x-1)x+2x+2

y=(x−1)x+2x+2

2 Regroup terms.

y=x(x-1)+2x+2

y=x(x−1)+2x+2

3 Expand.

y={x}^{2}-x+2x+2

y=x

2

−x+2x+2

4 Simplify  {x}^{2}-x+2x+2x

2

−x+2x+2  to  {x}^{2}+x+2x

2

+x+2.

y={x}^{2}+x+2

y=x

2

+x+2

5 Move all terms to one side.

y-{x}^{2}-x-2=0

y−x

2

−x−2=0

6 Use the Quadratic Formula.

x=\frac{1+\sqrt{4y-7}}{-2},\frac{1-\sqrt{4y-7}}{-2}

x=

−2

1+

4y−7

​

​

,

−2

1−

4y−7

​

​

7 Simplify solutions.

x=-\frac{1+\sqrt{4y-7}}{2},-\frac{1-\sqrt{4y-7}}{2}

x=−

2

1+

4y−7

​

​

,−

2

1−

4y−7

​

​

Done

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)