Solve x² - 4x - 7 = 0 by completing the square. What are the solutions?

Solution:

The equation given is

x² - 4x - 7 = 0

By taking 7 on the RHS

x² - 4x = 7

We know that

2ab = -4x

2xb = -4x

b = -2

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

x² - 4x + (-2)² = 7 + (-2)²

x² - 4x + 4 = 7 + 4

x² - 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.

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Solve x² - 4x - 7 = 0 by completing the square. What are the solutions?

Summary:

Solving x² - 4x - 7 = 0 by completing the square, the solutions are x = ±√11 + 2.