Identify coefficients: Identify the coefficients a, b, and c in the quadratic expression ax2+bx+c.a=139.254, b=−30000, c=−214642.1312.
Find two numbers: Look for two numbers that multiply to a⋅c (139.254⋅−214642.1312) and add up to b (−30000).This step involves trial and error or the use of a calculator.
Consider quadratic formula: After trying different combinations, realize that factoring this quadratic by finding two numbers that multiply to a⋅c and add to b is not straightforward.Consider using the quadratic formula instead.
Calculate discriminant: The quadratic formula is x=2a−b±b2−4ac. Calculate the discriminant b2−4ac. Discriminant = (−30000)2−4×139.254×(−214642.1312).
Perform correct calculation: Perform the calculation for the discriminant.Discriminant = 900000000−4×139.254×(−214642.1312).
Perform correct calculation: Perform the calculation for the discriminant. Discriminant = 900000000−4×139.254×(−214642.1312).Realize there's a mistake in the previous step, the calculation of the discriminant was not completed.