Chapter 4.5, Problem 58HP

To determine

To find: the person who solve the equation correctly using completing the square.

Answer to Problem 58HP

Alonso is correct and Aida is wrong.

Explanation of Solution

Given:

  

Concept used:

To solve the ${\text{ax}}^{\text{2}}\text{+bx+c=0}$ by completing the square:

1. Transform the equation so that the constant term $\text{c}$, is alone on the right side.
2. If $\text{a}$ ,the leading coefficient of ${\text{x}}^2$ term is not equal to $1$ , divide both side by $\text{a}$ .
3. Add the square of half the coefficient of the x term, ${\left(\frac{\text{b}}{\text{2a}}\right)}^{\text{2}}$ to both sides of the equation.
4. Factor the left side as the square of binomial.
5. Take the square root on both sides and remember: ${\left(\text{x+q}\right)}^{\text{2}}\text{=r}$ Is equivalent to $\left(\text{x+q}\right)\text{=±}\sqrt{\text{r}}$ .

Calculation:

According to the problem solved by Alonso and Aida

Here Alonso was correct in how he solved the equation ${\text{x}}^{\text{2}}\text{+8x-20=0}$ .

Aida forgot to add the result in finding the perfect square for both sides.

Since, this is an equation, anything added in the left side of the equation should also be added same in the right side of the equation.

Here Aida did add $\text{16}$ on left hand side of the 3^rd steps and forgot to add the same $\text{16}$ on the right hand side.

Hence Alonso is correct and Aida is wrong.