Use the Legs and Hypotenuse to find x

The legs of a right triangle are 4 cm and x cm.  The hypotenuse is (2x - 1) cm.  What is x?
A.)  7/6
B.)  4/3
C.)  5/3
D.)  3
E.)  5

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Use the Pythagorean Theorem
a² + b² = c²   {in a right triangle, a and b are the legs, and c is the hypotenuse (across from right angle)}

x² + 4² = (2x - 1)²   {substituted legs and hypotenuse into Pythagorean Theorem}
x² + 16 = (2x - 1)(2x - 1)   {when squaring a binomial, multiply it by itself}
x² + 16 = 4x² - 4x + 1   {used foil method}
3x² - 4x - 15 = 0   {subtracted x² and 16 from each side}
3x² - 9x + 5x - 15 = 0   {split -4x into -9x and 5x, factoring by grouping}
3x(x - 3) + 5(x - 3)   {factored 3x out of first two terms and 5 out of last two terms}
(x - 3)(3x + 5) = 0   {factored (x - 3) out of the two terms}
x - 3 = 0 or 3x + 5 = 0   {set each factor equal to 0}
x = 3   or   3x = -5    {added 3 and subtracted 5}
x = 3   or   x = -5/3   {divided second equation by 3}

x is a leg of a triangle and cannot be negative

x = 3

D.)  3

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