Solving x^2 – 8x + 16: Factoring and Quadratic Formula Methods

x^2 – 8x + 16

To find the value of the expression x^2 – 8x + 16, we can factorize it or solve it using the quadratic formula

To find the value of the expression x^2 – 8x + 16, we can factorize it or solve it using the quadratic formula. Let’s look at both methods:

Method 1: Factoring

To factorize x^2 – 8x + 16, we need to find two numbers that when multiplied give us 16, and when added give us -8 (the coefficient of x).

The factors of 16 are:
1, 2, 4, 8, 16

By testing these factors, we find that 4 and 4 satisfy the conditions. So, we can rewrite the original expression as:

(x – 4)(x – 4)

Method 2: Quadratic Formula

The quadratic formula is given by:

x = (-b ± √(b^2 – 4ac)) / (2a)

In our case, a = 1, b = -8, and c = 16. Let’s substitute these values into the formula:

x = (-(-8) ± √((-8)^2 – 4(1)(16))) / (2(1))
x = (8 ± √(64 – 64)) / 2
x = (8 ± √0) / 2

Since the discriminant (√(b^2 – 4ac)) is 0, this quadratic equation has equal roots.

Therefore, x = 8 / 2 = 4.

So, the solutions to the equation x^2 – 8x + 16 are x = 4.

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