By plotting appropriate graphs, find x to the nearest integer if x^2+3=2-4x.

Plot the graphs y=x^2+3 and y=2-4x. The solution(s) are the point(s) of intersection. The graphs can be plotted by making a table of values; this is the best method for the quadratic curve. The straight line may be more quickly plotted by recognising the coefficient of x gives the gradient and the intercept is 2, though finding and plotting appropriate values would also be successful. When plotting these graphs it is important to choose an appropriate scale; you must recognise that a quadratic equation of this type may have multiple solutions so allow for a wide range of values, but also be able to find the answers to the nearest integer (whole number).