Chapter 9, Problem 25MCQ

To determine

To solve the given equation by completing the square.

Answer to Problem 25MCQ

The values of x are $-3.4$ and $-0.6$ .

Explanation of Solution

Given information :

The function provided is $x^2+4x+2=0$ .

Formula used :

To solve an equation by completing the square, divide the coefficient of x of the equation by 2 and square it. That should provide the constant value. Then the equation would be of the form ${\left(x+\frac{b}{2}\right)}^2$ . Adjust the other constants and then square root the left-hand and right-hand sides. This would give the values of the equation.

Calculation :

  $x^2+4x+2=0$

Given equation.

Here $b=4$ , the coefficient of x.

  $\frac{b}{2}=\frac{4}{2}$

  $=2$

For making the expression a perfect square.

  ${\left(\frac{b}{2}\right)}^2={\left(\frac{4}{2}\right)}^2=4$

This is the value of the constant.

  $x^2+4x=-2$

Make left hand side a perfect square using the value of b.

  $=>x^2+4x+4=-2+4$

Adjust the values accordingly

  $=>{\left(x+2\right)}^2=2$

Taking square root.

  $=>\left(x+2\right)=\pm \sqrt{2}$

Compute the values.

  $=>\left(x+2\right)=\pm 1.4$

Now, equate both values, to get the answers of x.

  $=>x+2=1.4$

Simplify for x.

  $=>x=1.4-2$

  $=>x=-0.6$

This one value.

  $x+2=-1.4$

Computing the other value.

  $=>x=-1.4-2$

Simplify

  $=>x=-3.4$