What are the solutions to the equation? 4x=32-x^2

-8 and 4

Step-by-step explanation:

4x=32-x^2 x^2 + 4x - 32=0 x^2+4x+4 - 36=0 (x+2) ^2 - 6^2=0 (x+2+6) (x+2-6) = 0 x+8=0 ⇒ x = - 8 x-4=0 ⇒ x=4

4x = 32 - x^2

Subtract 4x from both sides and rearrange the equation:

-x^2 - 4x + 32 = 0

Use the quadratic equation x = - b + / - sqrt (b^2-4ac) / 2a

From the rewritten equation: a=-1, b = - 4 and c = 32

Solving for x you get x = - 8 and x = 4

The solutions are - 8 and 4