Solve: s = 4 + √ s + 2 a. s=2 b. s=7 c. s=2 or s=7 d. no real solution

You can use the formula for solutions of a quadratic equation to find the solution to the given equation.

The solution to the given equation is given by:

Option B : s = 7

A quadratic equation is an equation which can be arranged in the standard form   where a, b and c are real numbers and is variable.

The of    is given by:

We can see that there is a square root. We can take that root term on one side and can square both the sides, ending up on the quadratic equation.

You need to notice the most important fact here:

We could've ended up on the same quadratic equation if we start from

This is because    

Thus, from the solutions we will get from the quadratic equation, only one will belong to since other solution will belong to thee equation . We will have to check which solution is correct solution to the given equation.

Comparing the obtained quadratic equation with the standard form of quadratic equation, we get:

a = 1 (as there is always 1 multiplied with all terms)

b = -9

c = 14

Thus, the solutions are:

Checking solutions:

and

Thus, s = 7 is the solution to the given equation.

The solution s = 2 is for other equation

Thus,

The solution to the given equation is given by:

Option B : s = 7

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Rewrite s = 4 + sqrt(s+2) as s-4 = sqrt(s+2)

Square both sides: s^2 - 8s + 16 = s + 2

combine like terms: s^2 - 9s + 14 = 0

Factor this: (s-7)(s-2)=0

Solve for s: s={7, 2}

b. astronomers