There are many possible sets of "steps to solution." One is to use a graphing calculator to draw a graph of the equation given by the problem statement.
Another is to let your graphing calculator solve it. (See the image below.)
Another is to write the equation and solve it by any of several means.
.. x^2 -x = 210
.. x^2 -x +0.25 = 210.25 . . . . . add 1/4 to complete the square
.. (x -0.5)^2 = 210.25
.. x = 0.5 ±√210.25
.. x = 0.5 ±14.5
.. x = -14, +15
.. x^2 -x -210 = 0
.. (x -15)(x +14) = 0 . . . . . factor the equation
.. x = -14, 15
.. x^2 -x -210 = 0
.. x = (1 ±√(1 -4*1*(-210)))/(2*1) . . . . . use the quadratic formula
.. x = (1 ±√841)/2
.. x = (1 ±29)/2
.. x = -14, 15
Another is to use estimation. You know the difference factors as
.. x^2 -x = 210
.. x(x -1) = 210
So any integer values of x will be very near (the square root of 210) ±0.5 (see 'completing the square', above, for the exact solution). That is
.. √210 ≈ ±14.49 ≈ ±14.5
so we can expect the numbers x and (x-1) to be 15 and 14, or -14 and -15. When we check, we find the products of these pairs to be 210.
