Consider the following quadratic equation. (x+3)^2=43 When taking the square root of both sides, how many solutions will the equation have?

(x + 3)² = 43

Taking square root on both sides :
x + 3 = √43 or x + 3 = -√43

Rearrange and thus :
x = -3 + √43 or x + 3 = -3 - √43

There are TWO solutions.

( x + 3) ^ 2 = 43

Taking square root both sides,

(x+3) = (43) ^ (1/2)

x + 3 = 43 ^ (1/2) or x + 3 = - 43 ^ (1/2) { because square root of a number has both positive and negative values}

x = - 3 + 43 ^ (1 / 2) or x = - 3 - 43 ^ (1/2)

2 solutions

Okay.

(x + 3)^2 = 43
x^2 + 6x - 34 = 0
x
= [-6 ± √(36 + 136)]/2
= -3 ± √43
The equation has two solutions.

Two answers. The square root of 43 has two answers. Approx 6.5 and approx -6.5

(x+3)^2=43
If you take the square root of both sides, you get:

(x+3) = ±sqrt(43), which means there are two solutions.

Since this is a second order polynomial if you expanded the left side, it can have a maximum of 2 solutions