Answer:
Heya
Explanation:
To find the equation that is equivalent to (2x + 3)² - 14x - 21 = -6 in terms of m, we need to substitute m with 2x + 3.
Let's substitute m = 2x + 3 into the equation:
(2x + 3)² - 14x - 21 = -6
Expanding the square of (2x + 3):
(4x² + 12x + 9) - 14x - 21 = -6
Simplifying the equation:
4x² - 2x - 18 = -6
Bringing all terms to one side:
4x² - 2x - 18 + 6 = 0
Combining like terms:
4x² - 2x - 12 = 0
Now we have the equation in terms of x. To find the equation in terms of m, we need to substitute back m = 2x + 3.
Let's substitute m = 2x + 3 into the equation:
4(2x + 3)² - 2(2x + 3) - 12 = 0
Expanding the square of (2x + 3):
4(4x² + 12x + 9) - 4x - 6 - 12 = 0
Simplifying the equation:
16x² + 48x + 36 - 4x - 6 - 12 = 0
Combining like terms:
16x² + 44x + 18 = 0
Now we have the equation in terms of m. Simplifying further, we get:
m² + 7m - 15 = 0
Therefore, the equivalent equation in terms of m is (C) m² + 7m - 15 = 0.