Final answer:
The correct substitution of the values a = 1.00, b = 10.0, and c = -200 into the quadratic formula is: x = (-b ± √(b^2 - 4ac)) / (2a). Substituting the given values, we have x = -5.0 ± 15.0. Therefore, the solutions to the equation 1 = -2x + 3x^2 + 1 are x = -20.0 and x = 10.0.
Step-by-step explanation:
The correct substitution of the values a = 1.00, b = 10.0, and c = -200 into the quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the given values, we have:
x = (-10.0 ± √((10.0)^2 - 4(1.00)(-200))) / (2(1.00))
x = (-10.0 ± √(100.0 + 800.0)) / 2.00
x = (-10.0 ± √900.0) / 2.00
x = (-10.0 ± 30.0) / 2.00
x = -5.0 ± 15.0
Therefore, the solutions to the equation 1 = -2x + 3x^2 + 1 are x = -20.0 and x = 10.0.