four times a number is five less than the square of that number, Find the negative solution

Question

i'm new to these types of questions and i have no clue how to answer this, can you guys help?

Answer 1

Let x be the number. Stating the problem as an equation:

 

4x = x² - 5     (Rearrange the equation to form a quadratic -(subtract 4x from both sides))

 

x² - 4x -5 = 0    (Either factor the equation, or use the standard solution for a quadratic equation. In this case, it can be                               factored.)

(x - 5) (x + 1) = 0,   Set each factor equal to zero to find the roots (the x values where the graph crosses the x axis)

 

                                 These values were x = 5, and x = -1, one positive root and one negative root. The negative                                        solution of these two solutions is -1.