Question

Rewrite the equation by completing the square 3+x=x^2+3x

Answer 1

Answer:

$(x+1)^2=4$

Step-by-step explanation:

• $3+x=x^2+3x$ is our equation
• first, get all the x terms on one side so the equation equals a constant number
• $3+x-(x)=x^2+3x-x\\3=x^2+2x\\x^2+2x=3$
• Then add to both sides the square of half of the coefficient of x : the coefficient of x here is 2 so
• the square of half of 2 is $(1)^2$ then
• $x^2+2x+(1)^2=3+(1)^2\\x^2+2x+1=4$
• If you factor the left side you get
• $x^2+2x+1=4\\(x+1)^2=4$