Answer: x = 4 and x = -3/2
Procedure:
1) Given: 2x^2 - 5x - 12 = 0
2) Multiply both sides by : 2(2x^2) - 2(5x) - 2(12) = 0
3) Rearrange: (2x)^2 -5(2x) - 24 = 0
4) Notice that the common factor is (2x)
5) Set the parenthesis with the common factor inside:
(2x ) (2x ) =0
6) The first sign is the same sign of the second term of the trinomial, which is negative, the second sign is the product of the signs of the second and the third terms of the polynomial, which is (-)*(-) = + (positive)
(2x - )(2x + ) = 0
7) find two numbers that sum up - 5x and its product is -24.
- 8 + 3 = - 5
(-8)(+3) = -24
=> the numbers in the factors are -8 and +3
(2x - 8) (2x + 3) = 0
That is the factored equation. Now you can solve
8) a) 2x - 8 = 0 => 2x = 8 => x = 8/2 => x = 4
b) 2x + 3 = 0 => 2x = - 3 => x = - 3/2
Answer: the two solutions are x = 4 and x = -3/2
Given the equation, 5x + 22 = 27:
The goal is to isolate the variable. Hence, a few mathematical operations are necessary to solve for the value of x.
Start by subtracting 22 both sides:
5x + 22 - 22 = 27 - 22
5x + 0 = 5
5x = 5
Next, divide both sides by 5 to isolate and solve for the value of x:
5x/5 = 5/5
x = 1
In order to verify whether x = 1 satisfies the give equation, we must substitute its value into the given equation:
5x + 22 = 27
5(1) + 22 = 27
5 + 22 = 27
27 = 27 (True statement. This implies that x = 1 is the correct value that satisfies the equation).
Therefore, the correct answer is x = 1.
Answer:
315 miles
Step-by-step explanation:
450 (total miles) x (since they said "of", you multiple) 70% (amount completed) gives you 315 miles.
Answer:
QTS=STQ=STR
Step-by-step explanation:
