Solve x^2+5x+6 = 0

Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.

Equation
Answer
x = -3, -2

x2+5x+6=0

Solve by factoring the quadratic and applying the zero product property:

Step 1 — Factor the quadratic

We need two numbers that multiply to 6 (the constant term) and add to 5 (the coefficient of x):

3 × 2 = 6 and 3 + 2 = 5

Write the factored form using these numbers:

(x + 2)(x + 3) = 0

Step 2 — Apply the zero product property

If a product equals zero, at least one of the factors must be zero. Set each factor equal to zero and solve:

x + 2 = 0 → x = −2

x + 3 = 0 → x = −3

x = -3, -2

-6 -4 -2 2 4 2.5 5 7.5 10 12.5 15 x = -5/2 (-3, 0) (-2, 0) vertex (-5/2, -1/4) (0, 6)

How to solve x^2+5x+6 = 0

To solve x^2+5x+6 = 0, we can try factoring, use the quadratic formula, or complete the square. The solution is x = -3, -2.

This is a second-degree quadratic equation — the highest power of the variable is 2. Quadratic equations can have two real roots, one repeated root, or two complex roots.

Frequently asked questions

What is the answer to x^2+5x+6 = 0?
The answer is x = -3, -2.

What method is used?
factoring when possible, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the number and type of solutions.

How do I verify this?
Substituting the solution(s) back into x^2+5x+6 = 0 confirms both sides are equal.

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