Answer:
x = -2 or x = 12
Explanation:
Using factorisation method, we need two numbers that add up to -10, but the same two numbers multiply with one another to produce answer of -24.
Format is (x ) (x ) = 0
-12 and 2, when added, produce result of -10.
When multiplied, they give result of -24
(x + 2) (x – 12) = 0. We have x + 2 = 0, x = -2. We also have x – 12 = 0, x = 12.
x = -2 and x =12 are the solutions of the equation.
We can check if we are correct by ‘multiplying out’ the brackets.
(x + 2) (x – 12) = X² - 12x + 2x + (2 X -12)
= x² – 10x - 24. 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 = -10, c = -24
x = (-b ± √(b² - 4ac) ÷ 2a)
= (-(-10) ± √((-10)² - 4(1)(-24)) ÷ 2(1))
= ((10 ± √(100 + 96)) ÷ 2)
= (10 ± √196) ÷ 2
= (10 ± √(4 X 49)) ÷ 2
= (10 ± √4 X √49) ÷ 2
= (10 ± 2 X 7) ÷ 2
= (10 ± 14) ÷ 2
= 12 or -2.
Exactly what we got before.
Completing the square:
X² - 10x - 24 = 0
1) put the x, not ^2, in parenthesis.
2) half the coefficient (10) of x. that is 5. Put that into same parenthesis.
3) we have (x - 5)
4) square this and multiply out. (x - 5)² = X² - 5x - 5x +25 = X² - 10x + 25
5) this looks just like the original equation except for +25. What do we have to do to get back to original? from +25 to -24 is a gap of 49. so we have to subtract 49.
6) now we have (X - 5)² – 49 =0
7) (x - 5)² = 49
8) (x - 5) = ± √49
9) x = ± 7 + 5
= ± 7 + 5
= 12 or -2