Chapter 9, Problem 26MCQ

To determine

To solve the given equation by completing the square.

Answer to Problem 26MCQ

The values of x are $-2.3$ and $4.3$ .

Explanation of Solution

Given information :

The function provided is $x^2-2x-10=0$ .

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 :

  $x^2-2x-10=0$

Given equation.

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.

  $x^2-2x=10$

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

  $=>x^2-2x+1=10+1$

Adjust the values accordingly

  $=>{\left(x-1\right)}^2=11$

Taking square root.

  $=>\left(x-1\right)=\pm \sqrt{11}$

Compute the values.

  $=>\left(x-1\right)=\pm 3.3$

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

  $=>x-1=3.3$

Simplify for x.

  $=>x=4.3$

This one value.

Computing the other value.

  $x-1=-3.3$

Simplify

  $=>x=-2.3$