Question 1060594
Write and solve a quadratic equation. A right triangle has a hypotenuse of 105 inches. One leg is forty-two inches less than double the other leg. What is the length of the shorter leg? (Hint: a^2+b^2=c^2) 

I just need help with this question. If you could show step by step that would be perfect thanks!
<pre>The "other" leg is the shorter leg, which we'll call, S
Then the longer leg = 2S - 42
Using pythag theorem, {{{a^2 + b^2 = c^2}}}, we get: {{{highlight_green(S^2 + (2S - 42)^2 = 105^2)}}}
{{{S^2 + 4S^2 - 168S + "1,764" = "11,025"}}} ------ FOILing {{{(2S - 42)^2}}}
{{{5S^2 - 168S + "1,764" - "11,025" = 0}}}
{{{matrix(1,2, "**", 5S^2 - 168S - "9,261" = 0)}}}
{{{5S^2 - 315S + 147S - "9,261" = 0}}} ------ Replacing - 168S with  - 315S + 147S
5S(S - 63) + 147(S - 63) = 0
(S - 63)(5S + 147) = 0
S - 63 = 0                   OR                5S + 147 = 0
S, or length of the shorter leg = {{{highlight_green(matrix(1,2, 63, inches))}}}            OR              {{{S = - 147/5}}} (ignore)

** You could also solve this quadratic equation by: using the quadratic equation formula, COMPLETING THE SQUARE, or GRAPHING. However, graphing is most-often not used.