Solve for x in the equation x2 + 2x + 1 = 17.

The value of x in the equation is x = -5.123 or 3.123

Solution:

There are two ways to solve this equation.

We can either factorize it or use the quadratic equation. For factorizing it, it has to satisfy certain conditions

The condition is  should be a perfect square otherwise the equation is not factorable.

We have to rearrange the given equation to find values of a, b and c.

 ----- eqn 1

From eqn 1:

a = 1

b = 2

c = -16

Which is not a perfect square.

Hence we have to use the quadratic equation  formula, which is:

By substituting the values of a, b and in the quadratic equations. We get;

The two roots of x are:

On solving both the equations we will get the roots of the given equation, which are:

x = -5.123 or 3.123

Thus the value of "x" is found out

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752