Answer:
m² + 7m + 12 = 0 is equivalent to (5x - 2)² + 35x - 14 = -12 ⇒ C
Explanation:
To solve this problem substitute m by 5x - 2 in each answer to find which one give you the equation of x
The given equation is (5x - 2)² + 35x - 14 = -12
Let us start with answer A
∵ m² - 7m + 12 = 0
∵ m = 5x - 2
- Substitute m by 5x - 2
∴ (5x - 2)² - 7(5x - 2) + 12 = 0
- Simplify the middle term
∵ - 7(5x - 2) = - 7(5x) + - 7(-2)
∴ - 7(5x - 2) = - 35x + 14
- Substitute - 35x + 14 in the equation
∴ (5x - 2)² - 35x + 14 + 12 = 0
- Subtract 12 from both sides
∴ (5x - 2)² - 35x + 14 = -12 ⇒ Not equal to the given equation
Let us check answer B
∵ m² - 7m - 2 = 0
∵ m = 5x - 2
- Substitute m by 5x - 2
∴ (5x - 2)² - 7(5x - 2) - 2 = 0
- Simplify the middle term
∴ -7(5x - 2) = - 35x + 14
- Substitute - 35x + 14 in the equation
∴ (5x - 2)² - 35x + 14 - 2 = 0
- Add 2 to both sides
∴ (5x - 2)² - 35x + 14 = 2 ⇒ Not equal to the given equation
Now let us check answer C
∵ m² + 7m + 12 = 0
∵ m = 5x - 2
- Substitute m by 5x - 2
∴ (5x - 2)² + 7(5x - 2) + 12 = 0
- Simplify the middle term
∵ 7(5x - 2) = 7(5x) + 7(-2)
∴ 7(5x - 2) = 35x - 14
- Substitute 35x - 14 in the equation
∴ (5x - 2)² + 35x - 14 + 12 = 0
- Subtract 12 from both sides
∴ (5x - 2)² + 35x - 14 = -12 ⇒ Equal to the given equation
Let us check answer D
∵ m² + 7m - 2 = 0
∵ m = 5x - 2
- Substitute m by 5x - 2
∴ (5x - 2)² + 7(5x - 2) - 2 = 0
- Simplify the middle term
∴ 7(5x - 2) = 35x - 14
- Substitute 35x - 14 in the equation
∴ (5x - 2)² + 35x - 14 - 2 = 0
- Add 2 to both sides
∴ (5x - 2)² + 35x - 14 = 2 ⇒ Not equal to the given equation
m² + 7m + 12 = 0 is equivalent to (5x - 2)² + 35x - 14 = -12