Answer:
x is approximately equal to 1.09 and -3.43.
Step-by-step explanation:
I'm going to assume here that the "e" in question is the constant e ≈ 2.71828
In that case let's solve it by completing the square.
ex² - 7x² - 10x + 16 = 0
(e - 7)x² - 10x + 16 = 0
At this point, for simplicity, I'm going to refer to e - 7 as c, given that it's a constant number (roughly -4.28173). So we'll rewrite that as:
cx² - 10x + 16 = 0
cx² - 10x = -16
c²x² - 10cx = -16c
c²x² - 10cx + 25 = -16c + 25
(cx - 5)² = 25 - 16c
cx - 5 = ± √(25 - 16c)
cx = 5 ± √(25 - 16c)
x = (5 ± √(25 - 16c)) / c
Now we can plug the value of "c" back in and solve for x:
x = (5 ± √(25 - 16(e - 7))) / (e - 7)
x ≈ (5 ± √(25 + 16 × 4.28173)) / -4.28173
x ≈ (5 ± √93.50768) / -4.28173
x ≈ (5 ± 9.67) / -4.28173
x ≈ 14.67 / -4.28 ≈ -3.43
x ≈ -4.67 / -4.28 ≈ 1.09
So x is approximately equal to 1.09 and -3.43.
