Answer:
see explanation
Step-by-step explanation:
Using the method of completing the square.
Given
f(x) = x² + 4x - 6
add/subtract ( half the coefficient of the x- term )² to x² + 4x
f(x) = x² + 2(2)x 6 + 4 - 4 - 6
= (x + 2)² - 10
with m = 2 and n = - 10
To solve the equation let f(x) = 0 , that is
(x + 2)² - 10 = 0 ( add 10 to both sides )
(x + 2)² = 10 ( take the square root of both sides )
x + 2 = ± [tex]\sqrt{10}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{10}[/tex]
The positive solution is
x = - 2+ [tex]\sqrt{10}[/tex] ≈ 1.16 ( to 2 dec. places )
