What are the two solutions of x2 – 2x – 4 = –3x + 9?

  x = -0.5 ± √13.25 ≈ {-4.14005, 3.14005}

Step-by-step explanation:

If the only requirement is for a solution, I like to let a graphing calculator help out. Solving by hand or with a calculator, it is convenient to write the equation in standard form. The right side can be subtracted to give ...

  x² +x -13 = 0

The vertex can be found by adding and subtracting the square of half the x-coefficient:

  (x² +x +0.25) -13 -0.25 = 0

  (x +0.5)² -13.25 = 0

The vertex is (-0.5, -13.25). The coefficient of the x² term is 1, so the vertex form of the equation can lead directly to the solutions. Adding 13.25 to the equation and taking the square root gives ...

  (x +0.5)² = 13.25

  x = -0.5 ± √13.25