solve the followinh quadratic equation using square roots: (c+36)^2 - 38 = 251

Answer 1

To solve the quadratic equation, we can rearrange the equation as follows:

(c + 36)^2 - 38 = 251

First, let's move the constant term to the other side of the equation:

(c + 36)^2 = 251 + 38

(c + 36)^2 = 289

Next, we take the square root of both sides of the equation:

√((c + 36)^2) = ±√289

Since the square root of 289 is 17, we have:

c + 36 = ±17

Now, we can solve for c by subtracting 36 from both sides of the equation for each case:

Case 1: c + 36 = 17

Subtracting 36 from both sides, we get:

c = 17 - 36
c = -19

Case 2: c + 36 = -17

Subtracting 36 from both sides, we get:

c = -17 - 36
c = -53

Therefore, the two solutions to the given quadratic equation are c = -19 and c = -53.