Solve x^2+4x+4 = 0

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

Equation

Answer

x = -2

x²+4x+4=0

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

Step 1 — Factor the quadratic

We need two numbers that multiply to 4 (the constant term) and add to 4 (the coefficient of x):

2 × 2 = 4 and 2 + 2 = 4

Write the factored form using these numbers:

(x + 2)² = 0

Step 2 — Solve for zero

For this to equal zero, the base must be zero:

x + 2 = 0 → x = −2

x = -2

How to solve x^2+4x+4 = 0

To solve x^2+4x+4 = 0, we can try factoring, use the quadratic formula, or complete the square. The solution is x = -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+4x+4 = 0?
The answer is x = -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+4x+4 = 0 confirms both sides are equal.

More quadratic formula calculator problems

x² + 5x + 6 = 0 x² − 4 = 0 2x² − 3x − 2 = 0 x² + 2x − 8 = 0 x² − 6x + 9 = 0 3x² + x − 2 = 0 x² − 9 = 0 x² + 4x + 4 = 0 x² − x − 12 = 0 4x² − 1 = 0 x² + 3x = 10 2x² = 18