Answer: The required solution of the given equation is x = 9, -1 and rewritten equation is [tex]x^2+(-8)x=9.[/tex]
Step-by-step explanation: We are given to solve and rewrite the following quadratic equation so that it is in the form x² + bx = c :
[tex]x^2-8x-9=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To write the given quadratic equation in the required form, we need to take the constant term on the right-hand side of the equation.
From equation (i), we get
[tex]x^2-8x-9=0\\\\\Rightarrow x^2-8x=9\\\\\Rightarrow x^2-8x+16=9+16\\\\\Rightarrow (x-4)^2=25\\\\\Rightarrow x-4=\pm 5\\\\\Rightarrow x=4\pm5\\\\\Rightarrow x=4+5,~~4-5\\\\\Rightarrow x=9,~-1.[/tex]
Thus, the required solution of the given equation is x = 9, -1 and rewritten equation is [tex]x^2+(-8)x=9.[/tex]
