Solve using factorisation method

For a quadratic equation in the form $ax^2 + bx + c = 0$, the factorization method involves finding two numbers that multiply to $ac$ and add up to $b$.
In our simplified equation $x^2 + x - 150 = 0$, we have $a=1$, $b=1$, and $c=-150$.
We need to find two numbers that multiply to $1 \times (-150) = -150$ and add up to 1.

• Factors of 150: (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), (10, 15).
• We need two factors whose difference is 1 (since their product is negative and their sum is positive 1).
  • $150 - 1 = 149$
  • $75 - 2 = 73$
  • $50 - 3 = 47$
  • $30 - 5 = 25$
  • $25 - 6 = 19$
  • $15 - 10 = 5$

Since none of the integer factor pairs of 150 have a difference of 1, there are no two integers that multiply to -150 and add to 1. This means the quadratic expression $x^2 + x - 150$ cannot be factored into two linear factors with integer coefficients.

Therefore, the factorization method (using integer factors) is not suitable for solving this particular equation. The quadratic formula, as used in the previous solution, is the appropriate method for finding the exact solutions for this equation.