Answer: StartFraction negative 1 plus-or-minus StartRoot 21 EndRoot Over 2
Step-by-step explanation:
The given quadratic equation is expressed as
x² = 5 - x
Rearranging the equation to take the standard form of ax² + bx + c, it becomes
x² + x - 5 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1
b = 1
c = - 5
Therefore,
x = [- 1 ± √(1² - 4 × 1 × - 5)]/2 × 1
x = [- 1 ± √(1 - - 20)]/2
x = [- 1 ± √21]/2
x = (- 1 + √21)/2 or x = (- 1 - √21)/2
