Question

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

Answer 1

Step-by-step explanation:

I hope you can read my bad hand writing.

Answer 2

The value of x in the equation $x^{2}+2 x+1=17$ 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 $b^{2}-4 a c$  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.

$\begin{array}{l}{x^{2}+2 x+1=17} \\\\ {x^{2}+2 x+1-17=0}\end{array}$

$x^{2}+2 x-16=0$  ----- eqn 1

From eqn 1:

a = 1

b = 2

c = -16

$\text { Now substituting in } b^{2}-4 a c \text { we get; }$

$b^{2}-4 a c=2^{2}-4 \times 1 \times-16=4+64=68$

Which is not a perfect square.

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

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

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

$x=\frac{-2 \pm \sqrt{2^{2}-4 \times 1 \times-16}}{2 \times 1}$

$x=\frac{-2 \pm \sqrt{68}}{2 \times 1}$

The two roots of x are:

$\begin{aligned} x &=\frac{-2-\sqrt{68}}{2 \times 1} \\\\ x &=\frac{-2+\sqrt{68}}{2 \times 1} \end{aligned}$

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