# Solve x^{2} - 4x - 7 = 0 by completing the square. What are the solutions?

**Solution:**

The equation given is

x^{2} - 4x - 7 = 0

By taking 7 on the RHS

x^{2} - 4x = 7

We know that

2ab = -4x

2xb = -4x

b = -2

Let us take the square of b and add it to both sides

x^{2} - 4x + (-2)^{2} = 7 + (-2)^{2}

x^{2} - 4x + 4 = 7 + 4

x^{2} - 4x + 4 = 11

(x - 2)^{2} = 11

Taking square root on both sides

√(x - 2)^{2} = √11

(x - 2) = ±√11

x = ±√11 + 2

Therefore, the solutions are x = ±√11 + 2.

## Solve x^{2} - 4x - 7 = 0 by completing the square. What are the solutions?

**Summary:**

Solving x^{2} - 4x - 7 = 0 by completing the square, the solutions are x = ±√11 + 2.

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