Verified answer

1. y(y - 5) = 36

To solve this, expand the left side of the equation:

y^2 - 5y = 36

Move all terms to one side to get it in standard quadratic form:

y^2 - 5y - 36 = 0

Now, you can factor the quadratic:

(y - 9)(y + 4) = 0

Set each factor equal to zero and solve for y:

y - 9 = 0 --> y = 9

y + 4 = 0 --> y = -4

So, the solutions are y = 9 and y = -4.

2. (x + 3)(x - 2) = x + 10

Expand the left side:

x^2 + x - 6 = x + 10

Move all terms to one side:

x^2 + x - 6 - x - 10 = 0

Simplify:

x^2 - 16 = 0

Factor the quadratic:

(x - 4)(x + 4) = 0

Set each factor equal to zero and solve for x:

x - 4 = 0 --> x = 4

x + 4 = 0 --> x = -4

So, the solutions are x = 4 and x = -4.

3. (k + 5)^2 + (k - 2)^2 = 37

Expand and simplify the left side:

k^2 + 10k + 25 + k^2 - 4k + 4 = 37

Combine like terms:

2k^2 + 6k + 29 = 37

Subtract 37 from both sides:

2k^2 + 6k - 8 = 0

Divide the equation by 2 to simplify:

k^2 + 3k - 4 = 0

Factor the quadratic:

(k + 4)(k - 1) = 0

Set each factor equal to zero and solve for k:

k + 4 = 0 --> k = -4

k - 1 = 0 --> k = 1

So, the solutions are k = -4 and k = 1.

Im only in elem sorry can't help