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How to solve a quadratic equation x2 - 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 x2 - 10x + 24, by the method of completing the squares are x = 4 and x = 6.
Let's understand the solution in detail.
Given equation: x2 - 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, x2 - 10x + 25 - 25 + 24 = x2 - 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 x2 - 10x + 24 are x = 4 and x = 6.