How to Solve the Quadratic Expression x^2 – 10x + 24: Factoring and Quadratic Formula Methods

x^2 – 10x + 24

To solve the expression x^2 – 10x + 24, we can try factoring or using the quadratic formula

To solve the expression x^2 – 10x + 24, we can try factoring or using the quadratic formula.

Let’s start by factoring:

To factor the quadratic expression, we need to find two numbers whose product is 24 and whose sum is -10 (the coefficient of x).

Let’s list out the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

We can see that -4 and -6 are the two numbers that have a product of 24 and a sum of -10.

So, we can rewrite the expression as:

(x – 4)(x – 6)

Now, to solve the expression, we need to set each factor equal to zero and solve for x:

Setting x – 4 = 0, we add 4 to both sides:
x = 4

Setting x – 6 = 0, we add 6 to both sides:
x = 6

Therefore, the solutions to the expression x^2 – 10x + 24 are x = 4 and x = 6.

Alternatively, if factoring is not possible, we can use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 – 4ac)) / (2a)

For the expression x^2 – 10x + 24, the coefficients are a = 1, b = -10, and c = 24.

Plugging these values into the quadratic formula, we get:

x = (-(-10) ± √((-10)^2 – 4(1)(24))) / (2(1))
x = (10 ± √(100 – 96)) / 2
x = (10 ± √4) / 2
x = (10 ± 2) / 2

Simplifying further:

x = (10 + 2) / 2 = 12 / 2 = 6
x = (10 – 2) / 2 = 8 / 2 = 4

Again, we find the solutions to be x = 4 and x = 6.

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