Solving the Quadratic Equation x^2 + 5x + 6 = 0 using Factoring and Quadratic Formula

x^2 + 5x + 6

To solve the equation x^2 + 5x + 6 = 0, we can use the factoring method or the quadratic formula

To solve the equation x^2 + 5x + 6 = 0, we can use the factoring method or the quadratic formula.

Method 1: Factoring
To factor the quadratic expression x^2 + 5x + 6, we need to find two numbers that when multiplied give 6, and when added give 5. The numbers that satisfy these conditions are 2 and 3.

So, we can rewrite the equation as (x + 2)(x + 3) = 0.

Now, we set each factor equal to zero:
x + 2 = 0 –> x = -2
x + 3 = 0 –> x = -3

Therefore, the solutions to the equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.

Method 2: Quadratic formula
The quadratic formula is given by:

x = (-b ± √(b^2 – 4ac)) / (2a)

For the equation x^2 + 5x + 6 = 0, we have a = 1, b = 5, and c = 6. Plugging these values into the quadratic formula, we get:

x = (-5 ± √(5^2 – 4(1)(6))) / (2(1))
x = (-5 ± √(25 – 24)) / 2
x = (-5 ± √1) / 2

Simplifying further, we have:
x = (-5 + 1) / 2 or x = (-5 – 1) / 2
x = -4 / 2 or x = -6 / 2
x = -2 or x = -3

So, the solutions to the equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.

Both methods give the same results, x = -2 and x = -3, confirming that these are the solutions to the given quadratic equation.

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