Answer:
x = -2, x = 3
Explanation:
Using factorisation method, we need two numbers that add up to -1 (think of number in front of -x as -1, but the same two numbers multiply with one another to produce answer of -6.
Format is (x ) (x ) = 0
2 and -3, when added, produce result of -1.
When multiplied, they give result of -6.
(x + 2) (x – 3) = 0. We have x + 2 = 0, x = -2. We also have x – 3 = 0, x = 3.
X = -2 and x =3 are the solutions of the equation.
We can check if we are correct by ‘multiplying out’ the brackets.
(x + 2) (x – 3) = X ² - 3x + 2x + (2 X -3)
= x ² - x - 6. So, we are correct.
We could have solved this equation by using the quadratic formula.
x = ((-b ± √(b² - 4ac)) ÷ 2a)
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
NB number in front of x ² is just one. When no number is presented in front, it is just a 1. In this case, it is 1 x ² (simply just one lot of x ², or just x ²).
a = 1, b = -1, c = -6
x = (-b ± √(b² - 4ac) ÷ 2a)
= (-(-1) ± √((-1)² - 4(1)(-6)) ÷ 2(1))
= ((1 ± √(1 – -24)) ÷ 2)
= ((1 ± √(1 + 24)) ÷ 2)
= (1 ± √25) ÷ 2
= ((1 ± 5) ÷ 2)
= -2, 3.
Exactly what we got before.