# How to solve a quadratic equation x^{2} - 10x + 24 by completing the square?

Quadratic equations are those equations having a degree of two. They can have a maximum of two roots. They can be solved using the completing the square method.

## Answer: The solution of the quadratic equation x^{2} - 10x + 24, by the method of completing the squares are x = 4 and x = 6.

Let's understand the solution in detail.

**Explanation:**

Given equation: x^{2} - 10x + 24

Now, we follow the below steps to solve the problem using the method of completing the square:

- We identify the coefficient of x, which is 10. Now, we half and square the number, that is, (10/2)
^{2}= 25. - Now, we add and subtract 25 from the given equation, that is, x
^{2}- 10x + 25 - 25 + 24 = x^{2}- 10x + 25 - 1 - Now, we use the identity of (a - b)
^{2}and simplify the equation as: (x - 5)^{2}- 1 - Now, to find the roots, we equate the above equation to zero: (x - 5)
^{2}- 1 = 0 - Now, from the above equation, we get; x = 5 ± 1.
- Finally we have x = 5 + 1 = 6, and x = 5 - 1 = 4.

Hence, x = 4, 6

### Thus, the solutions of the quadratic equation x^{2} - 10x + 24 are x = 4 and x = 6.

Math worksheets and

visual curriculum

visual curriculum