Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 3x = 24


3.55, –6.55

3.62, –6.62

24.75, –27.75

4.66, 5.12

Answer 1

we have that
x² + 3x = 24
Group terms that contain the same variable
(x² + 3x) = 24
Complete the square. Remember to balance the equation by adding the same constants to each side
(x² + 3x+2.25) = 24+2.25

Rewrite as perfect squares

(x+1.5)² = 26.25
(+/-)[x+1.5]=5.12
(+)[x+1.5]=5.12----> x=5.12-1.5--->  x=3.62
(-)[x+1.5]=5.12-----> x=-1.5-5.12---> x=-6.62

the answer is
3.62, –6.62