Chapter 9, Problem 27MCQ

To determine

To solve the given equation by completing the square.

Answer to Problem 27MCQ

The values of x are -3.6 and 1.6 .

Explanation of Solution

Given information :

The function provided is $2x^2+4x-5=7$ . This can be written as $2x^2+4x-12=0$ .

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 :

  $2x^2+4x-12=0$

Given equation.

  $\frac{2x^2+4x-12}{2}=\frac{0}{2}$

Divide the equation by 2 such that the coefficient of $x^2$ becomes 1.

  $=>x^2+2x-6=0$

Here $b=2$ , the coefficient of x.

  $\frac{b}{2}=\frac{2}{2}$

  $=1$

For making the expression a perfect square.

  ${\left(\frac{b}{2}\right)}^2={\left(1\right)}^2=1$

This is the value of the constant.

  $x^2+2x=6$

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

  $=>x^2+2x+1=6+1$

Adjust the values accordingly

  $=>{\left(x+1\right)}^2=7$

Taking square root.

  $=>\left(x+1\right)=\pm \sqrt{7}$

Compute the values.

  $=>\left(x+1\right)=\pm 2.6$

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

  $=>x+1=2.6$

Simplify for x.

  $=>x=1.6$

This one value.

  $=>x+1=-2.6$

Computing the other value.

  $=>x=-3.6$