Mathematics, 14.07.2019 21:00 LuvieAnn1886

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

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Answer from: pukakchiu

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

What are the solutions of a quadratic equation?

A quadratic equation is an equation which can be arranged in the standard form ax^2 + bx + c = 0 where a, b and c are real numbers and is variable.

The of ax^2 + bx + c = 0 is given by:

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

How to find solution(s) of the given equation?

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.

$s = 4 + \sqrt{s+2}\\s-4 = \sqrt{s+2}\\\\\text{Squaring both sides}\\\\(s-4)^2 = (\sqrt{s+2})^2\\s^2 + 16 - 8s = s+2\\s^2 -9s + 14 = 0$

You need to notice the most important fact here:

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

$s = 4 - \sqrt{s+2}\\s - 4= -\sqrt{s+2}\\(s-4)^2 = (-\sqrt{s+2})^2\\s^2 + 16 - 8s = s + 2\\s^2 - 9s + 14 = 0$

This is because $(a)^2 = a^2\\and\\(-a)^2 = a^2$

Thus, from the solutions we will get from the quadratic equation, only one will belong to $s = 4 + \sqrt{s+2}$ since other solution will belong to thee equation $s = 4 - \sqrt{s+2}$ . 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:

$x = \dfrac{9 \pm \sqrt{81 - 56}}{2}\\\\x = \dfrac{9\pm \sqrt{25}}{2}\\\\x = \dfrac{9+5}{2}, x = \dfrac{9-5}{2}\\\\x = 7, x = 2$

Checking solutions:

$s = 4 + \sqrt{s+2}\\\text{Putting s = 7}\\7 = 4 + \sqrt{7+2}\\7 = 4 + \sqrt{9}\\7 = 4 + 3 = 7\\\text{Both sides same, thus correct solution}$

and

$s = 4 + \sqrt{s+2}\\\text{Putting = 2}\\2 = 4 + \sqrt{2+2}\\2 = 4 + \sqrt{4}\\2 = 4 + 2\\2 = 6 \\\text{The above statement is wrong, thus incorrect solution}$

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

The solution s = 2 is for other equation $s = 4 - \sqrt{s+2}$

Thus,

The solution to the given equation is given by:

Option B : s = 7

Learn more about quadratic equations here:
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Answer from: brittneyhiebert5583

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}

Answer from: Quest

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

Answer from: Quest

One shot. if 60% of 10 is 6, then what is 70%? we know it would be seven (since 60% is mathematically 60/100, or 6/10, then 70% is 70/100, or 7/10) but we can check anyway using ratios: 6 : 60% = x : 70%*inverse multiplicationx * 60% = 6 * 70%*divide both sides by 60%x = (6 * 70%) / 60%x = 7and since he has made 6 shots already, he would need just one more to get 7 shots or 70%. if the explanation is too confusing, comment and i will try to

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

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