Solve the equation by completing the square. round to the nearest hundredth if necessary? x^2+3x=24

X^2+3x=24, halve the linear coefficient, square it, and add it to both sides

In this case (3/2)^2=2.25

x^2+3x+2.25=26.25 now the left side is a perfect square...

(x+1.5)^2=26.25  take the square root of both sides

x+1.5=±√26.25  subtract 1.5 from both sides

x=-1.5±√26.25

x=-1.5-√26.25 and -1.5+√26.25

x≈ -6.62 and 3.62

a = 7 and c = 12

Step-by-step explanation:

Set up 2 equations and use substitution:

4a + 2c = 52

12a + 4c = 132

In the first equation, c = 26 - 2a

We can plug that into the second equation to solve for a.

12a + 4(26 - 2a) = 132

a = 7

Plug a back in to either original equation to solve for c:

4(7) + 2c = 52

c = 12