Answer:
[tex]\boxed{x = 2+2\sqrt{6} ~~or~~x = 2 - 2 \sqrt{6} }[/tex]
.
Step-by-step explanation:
To find x, use pythagoras form
[tex]c^2 = a^2 + b^2[/tex]
[tex](x + 4)^2 = x^2 + (x + 1)^2[/tex]
[tex]x^2 + 8x + 16 = x^2 + x^2 + 2x + 1[/tex]
[tex]2x^2 + 2x + 1 - x^2 - 8x - 16 = 0[/tex]
[tex]x^2 - 6x - 15 = 0[/tex]
[tex]x^2 - 6x = 15[/tex]
[tex](x - 3)^2 - 9 = 15[/tex]
[tex](x - 3)^2 = 15 + 9[/tex]
[tex](x - 3)^2 = 24[/tex]
[tex]x - 2 = \pm \sqrt{24}[/tex]
[tex]x = 2 \pm 2\sqrt{6}[/tex]
.
[tex]x_1 = 2 + 2\sqrt{6}[/tex]
[tex]x_2 = 2 - 2\sqrt{6}[/tex]
.
Happy to help :)
