How to Solve x^2 – 8x + 16: Factoring and Quadratic Formula Methods

x^2 – 8x + 16

To find the solution of the expression x^2 – 8x + 16, we can approach it in two ways:

1

To find the solution of the expression x^2 – 8x + 16, we can approach it in two ways:

1. Factoring:
We can try to factor the expression to find its solution. In this case, we are looking for two numbers that multiply together to give 16 and add up to -8. The numbers -4 and -4 satisfy these conditions. Therefore, we can factor the expression as:

(x – 4)(x – 4)

Or simplifying further:

(x – 4)^2

So, the solution to the expression x^2 – 8x + 16 is (x – 4)^2.

2. Quadratic formula:
Alternatively, we can use the quadratic formula to find the solution. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solution for x can be found using the formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

In our case, a = 1, b = -8, and c = 16. Plugging these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 – 4(1)(16))) / (2 * 1)

simplifying further:

x = (8 ± √(64 – 64)) / 2

x = (8 ± √0) / 2

Since the square root of 0 is 0, the expression simplifies to:

x = (8 ± 0) / 2

x = 8 / 2

x = 4

So, the solution to the expression x^2 – 8x + 16 is x = 4.

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