Solving the Quadratic Equation x^2 + 10x + 16: Factoring and Quadratic Formula Methods Explained

x^2 + 10x + 16

To solve the quadratic equation x^2 + 10x + 16, we can factorize it or use the quadratic formula

To solve the quadratic equation x^2 + 10x + 16, we can factorize it or use the quadratic formula.

1. Factoring:
In this case, we need to find two numbers whose product is 16 and whose sum is 10. The numbers are 2 and 8. We can rewrite the equation as:

x^2 + 2x + 8x + 16

Now, we group the terms and factor by grouping:

(x^2 + 2x) + (8x + 16)
x(x + 2) + 8(x + 2)

Notice that (x + 2) appears in both terms. We can factor it out:

(x + 2)(x + 8)

Therefore, x^2 + 10x + 16 can be factored as (x + 2)(x + 8).

2. Quadratic Formula:
Another method to solve the quadratic equation is by using the quadratic formula:

x = (-b ± √(b^2 – 4ac)) / (2a)

In this case, a = 1, b = 10, and c = 16. Substituting these values into the formula, we get:

x = (-(10) ± √((10)^2 – 4(1)(16))) / (2(1))
x = (-10 ± √(100 – 64)) / 2
x = (-10 ± √36) / 2
x = (-10 ± 6) / 2

Now we consider the two possible solutions:

Solution 1:
x = (-10 + 6) / 2
x = -4 / 2
x = -2

Solution 2:
x = (-10 – 6) / 2
x = -16 / 2
x = -8

Therefore, the solutions to the quadratic equation x^2 + 10x + 16 are x = -2 and x = -8.

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