a and b are legs of the triangle.
c is the hypotenuse of the triangle.
you are given:
a = x
b = x+1
c = x+3
you need to solve for x.
the attached file shows the progression.
number 1 shows the formula used.
number 2 simplifies the equation by multiplying the factors shown.
number 3 simplifies further by combining like terms.
number 4 moves everything from the right hand side of the eqution to the left hand side of the equation.
number 5 combines like terms.
number 6 places 8 to the right hand side of the equation to prepare for solving by completing the squares method.
number 7 reformats the equation into completing the square form.
number 8 combines like terms.
number 9 takes the square root of both sides of the equation.
number 10 shows you the results of the operation.
i tested the results by subsituting for x in the original equation and it checks out so i'm reasonably sure this is the right answer.
you may want to simplify square root of 12 by showing it as 2 times the square root of 3 (see number 11 in the attached file).
instructions for completing the square method can be found at this website.
http://webgraphing.com/quadraticequation_completingthesquare.jsp
you select solving by completing the squares method and enter the equation of x^2 - 4x - 8 = 0 into the box provide and click on solve it and your answer plus step by step instructions shows up.
if you would rather read how to do it, then go to the following link.
http://www.purplemath.com/modules/solvquad3.htm for instructions.