Final answer:
To solve the equation ax=b, we must have a quadratic formula with a non-negative discriminant. Given the constants a=1.00, b=10.0, and c=-200, the discriminant is positive, indicating that the equation is solvable and the value of c that makes this possible is -200.
Step-by-step explanation:
Finding the value of c in the quadratic equation ax=b
To find the value of c that allows us to solve the equation ax=b, we actually need to look at the quadratic equation ax²+bx+c = 0. The quadratic formula x = (-b ± √(b²-4ac))/(2a) is used to find the roots of this equation. For the quadratic equation to be solvable, the discriminant (the part under the square root, b²-4ac), must be non-negative.
Given the constants a = 1.00, b = 10.0, and c = -200, we can use the quadratic formula to solve for x. The discriminant here is 10.0² - 4(1.00)(-200) which equals 1000, a positive number. Therefore, the equation is solvable, and we can apply the quadratic formula to find the roots.
By plugging in the values into the quadratic formula, we get: x = (-10 ± √(1000))/2(1.00), which simplifies to two possible solutions for x. Therefore, the value of c that makes the equation solvable is -200.