Question

Solve the equation

x2 + 4x - 7 = 0
by completing the square.
Give your answers correct to 2 decimal places.

Answer 1

x ≈ 1.32, x ≈ - 5.32

Explanation:

Given

x² + 4x - 7 = 0 ( add 7 to both sides )

x² + 4x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 7 + 4

(x + 2)² = 11 ( take the square root of both sides )

x + 2 = ±
`\sqrt11}` ( subtract 2 from both sides )

x = - 2 ±
`√(11)`

Thus

x = - 2 -
`√(11)` ≈ - 5.32 ( to 2 dec. places )

x = - 2 +
`√(11)` ≈ 1.32 ( to 2 dec. places )