Question

Need help with solving quadratics using the quadratic equation!

See image, this is a word problem.

Answer 1

You need to solve the following equation:
-0.5x^2 +36x -161 = 451

Set right side to 0
-0.5x^2 +36x -612 = 0

Multiply by -2 to get rid of decimal and leading neg coefficient.
x^2 -72x + 1224 = 0

Use quadratic formula:
a = 1, b = -72, c = 1224


`x = (-(-72) \pm √((-72)^2 -4(1)(1224)))/(2(1)) \\ \\ x = (72 \pm √(288))/(2) \\ \\ x = 27.51, 44.49`

Therefore the min price to have 451 profit is $27.51