The questions is "The length and width of a rectangle are $7$m and $5$m. When each dimension is increased by the same amount, the area is tripled. Find the dimensions of the new triangle, to the nearest tenth of a metre."`
Answer: The rectangle is $9.3$m by $11.3$m
I started with writing: $(x+7)(x+5)=105$
Then I expanded to standard form: $x^2+12x-70$
Then I completed the square to convert this to vertex form: $(x+6)^2-106$
I thought that the vertex of the parabola was going to be the dimensions of the new rectangle, but it isn't. I then checked if the roots of this equation were the answer, but they weren't. Now I'm completely lost. Any help is appreciated, my final exams are in two days.