This is the question that's gonna put me over the top and make me a Brainly Genius. Of course working for free doing middle school math homework doesn't really sound like a genius, but I'm doing it anyway.
This one is the Pythagorean Theorem of course:
[tex](x+3)^2 + (x+4)^2 = (x+10)^2[/tex]
[tex]x^2 + 6x + 9 + x^2 + 8x + 16 = x^2 + 20 x + 100[/tex]
[tex]x^2 - 6x - 75 = 0[/tex]
The Shakespeare Quadratic Formula (2b or -2b) is a little shortcut for the quadratic formula when the middle term is even.
[tex]x^2-2bx+c \textrm{ has zeros } x=b\pm \sqrt{b^2-c}[/tex]
So we get
[tex] x = 3 \pm \sqrt{3^2 -(-75)} = 3 \pm \sqrt{84} = 3 \pm 2 \sqrt{21}[/tex]
The minus root is less than -6 giving negative sides, so we reject it and conclude
[tex]x = 3 + 2 \sqrt{21} [/tex]
Choice C
When I hit Add I officially become a Genius. Maybe I should retire.
