81x2 + 72x + 16 = 81x2 + 36x + 36x + 16 = 9x(9x + 4) + 4(9x + 4) = (9x + 4)2
Since the first and the last term happen to be perfect squares, you can take the square root of each, and check whether the linear term (the central term) happens to be twice the first term, times the last term. In this case it is.
http://wolfa.com/input/?i=72x-50y%2B188%3D0 72x-50y+188=0 Rewrite as 72x-50y=-188 x = -188/72 = -2.611 y = -188/-50 = 3.76 For more information and fraction form of the answer, see the link above
72x - 50y + 52z = -188-- At the x-intercept, 'y' and 'z' are zero.72x = -188x = -2.611...-- At the y-intercept, 'x' and 'z' are zero.-50y = -188y = 3.76-- At the z-intercept, 'x' and 'y' are zero.52z = -188z = -3.615 (rounded)
8x(x+9)
It is a quartic equation in the variable x.
2x + 3 = 72x = 4x = 2
35x^2 + 77x + 42 Improved answer: 5x+67x+7 When simplified = 72x+7
-64
7 (x+1)/72 = (x-1)/54 x+1 = (72x-72)54 54x+54 = 72x-72 54x-72x = -72-54 -18x = -126 x = 7
If a trinomial is a perfect square, then the discriminant will equal 0. The discriminant is equal to B^2-4AC. The variables come from the standard form of a quadratic which is Ax^2+Bx+C In this problem, A=81, B=-72, and C=16 so the discriminant is: (-72)^2-4(81)(16)=5,184-5,184=0 so this is a perfect square trinomial. To factor, notice that 81=9^2 and 16=4^2, so 81x^2=(9x)^2. We can then factor the trinomial into (9x+4)(9x-4)
72x-3=112x=14x=7
2x + 4y = 72x - 2x + 4y = 7 - 2x4y = -2x + 74y/4 = -2x/4 + 7/4y = -(1/2)x + 7/4Now that y is a function of x, you can give some values for x and find the corresponding values for y. (There are infinitely values for x an y)