Solve advanced and complicated equations using the power of graphs.

Problem

Let f, left parenthesis, x, right parenthesis, equals, 2, start superscript, x, start superscript, 2, end superscript, end superscript and let g, left parenthesis, x, right parenthesis, equals, minus, x, plus, 3.
The graph of y, equals, f, left parenthesis, x, right parenthesis is shown below.
Use the interactive graph to sketch a graph of y, equals, g, left parenthesis, x, right parenthesis.
Let x, start subscript, 1, end subscript and x, start subscript, 2, end subscript be solutions of 2, start superscript, x, start superscript, 2, end superscript, end superscript, equals, minus, x, plus, 3, where x, start subscript, 1, end subscript, is less than, x, start subscript, 2, end subscript.
Estimate the value of x, start subscript, 1, end subscript.
Answers within units of the solution will be accepted.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i