(1+?)**2=16

Question

Please haw can find

Answer 1

Hint: use the inverse operation of squaring a number.

Answer 2

(1+x)**2 = 16
(1+x)*(1+x) = 16
1+x+x+x^2 =16
x^2 + 2x + 1=16 |-16
x^2 + 2x - 15 = 0

pq-formula:

-2/2 +- √((2/2)^2-(-15))
<=> -1 +- √((1)+15)
<=> -1 +- √(16)

Now you have two solutions:

X1= -1 + √(16) = 3
X2= -1 - √(16) = -5

proove that solutions X1,2 are right:

X1: (3)^2 + 2(3) - 15 = 0
15 - 15 = 0

X2: (-5)^2 + 2(-5) - 15 = 0
25 - 25 = 0

Answer 3

When:
x = y

You need to think, that x is y, what ever changes you do on x, you can do for y, and their results are equal:
x + a = y + a
x - b = y - b
x*a*b = y*a*b

√x = √y
x+x = y+x
x**2 = y**2
(There is an exception that you should not multiply or divide by 0.)

When you want to solve a variable, (in your question it is "?"), you want do operations (on both sides), so that in 1 side there would only be the variable we want to solve.

(10 + ?) ** 2 = 64

We can take squareroot from both sides to simplify the expression:
(10 + ?) ** 2 = 64 ||√(...)
√((10 + ?) ** 2) = √(64)
10 + ? = (+/-) 8

(+/-) 8 meand that 8 can be positive or negative, squareroot √(x) means what multiplied by what equals x, because (-8)*(-8) = 64 and 8*8 = 64, we don't know whether the squareroot is negative or positive.

But now we can subtract 10 from both sides:
10 + ? = (+/-) 8 ||-10
10 + ? - 10 = (+/-) 8 - 10
? = (+/-) 8 - 10

And ? can either be:
? = +8 - 10 = -2
or:
? = -8 - 10 = -18