Answer:
x= [tex]4\pm \sqrt{73}[/tex]
Step-by-step explanation:
First step. Solve the binomial product from the left side of the equation:
[tex](x-12)(x+4)=9[/tex]
[tex]x^2+4x-12x-48=9[/tex]
Second step. Simplify and move independent terms to the right side of the equation:
[tex]x^2-8x=57[/tex]
Third step. Find a number that multiplied by two gives -8, then square this number and sum it on both sides of the equation:
[tex]x^2-8x+16=57+16[/tex]
Fourth step. Write the left side of the equation as a squared binomial:
[tex](x-4)^2=73[/tex]
Fifth step. First, take the square root and then add 4 to both sides of the equation to solve for x:
[tex](x-4)=\pm \sqrt{73}[/tex]
[tex]x= 4\pm \sqrt{73}[/tex]
