Question

1. Find the roots of the following quadratic equations, if they exist, by the method of
completing the square:
$x ^{2} + x - 4 =0$
​

Answer 1

$\sf{x^2+x-4=0}$

• Adding 4 to Both Sides

$\to\sf{x^2+x-4+4=0+4}$

• Simplify The Expression

$\to\sf{x^2+x=4}$

• Rewrite in the form of (x + a)² = b

$\to\sf{\displaystyle\left(x+\frac{1}{2}\right)^2=\frac{17}{4}}$

• For f²(x) = a, The Solutions are f(x) = √a , - √a

$\to\sf{\displaystyle x=\frac{\sqrt{17}-1}{2},\:x=\frac{-\sqrt{17}-1}{2}}$