Question

Solve the problem in the picture please

Answer 1

(1) y= - x² - 4x + 9 and (2) y + 5x = - 7. Isolate y in (2); y= - 5x - 7 (3)

Since (1) and (3) have the same value or the same y, then we can write:
(1)=(3)

- x² - 4x + 9 = - 5x - 7

-x² - 4x + 9 + 5x +7 = 0

-x² + x + 16 = 0  OR x² - x - 16 = 0

Solve this quadratic equation:

x' = [-b+√(b²-4ac)]/(2a) and x" = [-b-√(b²-4ac)]/(2a)

x' = [+1+√(-1)² - 4(1)(-16)]/2 → x' = [1+√(1+64)]/2 → x' = [1+√65)]/2
x" = [+1-√(-1)² - 4(1)(-16)]/2 → x' = [1-√(1+64)]/2 → x' = [1-√65)]/2

x' = [1+√65)]/2 = + 4.5311


x" =[1-√65)]/2 = - 3.5311