How does one solve the following equasion symbolically? 20-x^2=5x

Question

solve the system of equasion symbolically

Answer 1

20-x²=5x, x²+5x=20,

x²+2(5x/2)+(5/2)²=20+(5/2)²,

(x+5/2)²=20+25/4=105/4,

x+5/2=±√105/2, x=-5/2±√105/2, so x=-5/2+√105/2 or -5/2-√105/2. (√105=5.1235 approx.)

This result is symbolised by the x-intercepts on a graph of y=x²+5x-20 (parabola). The intercepts lie at equal distances from the axis of symmetry, x=-5/2.

Another way to symbolise this is to draw a graph of y=x²+5x and a horizontal line y=20. Where the line cuts the curve in two places are the two solutions for x.