To solve the equation
((x-225)/250)^2 + ((93*sqrt(1-((x-1.5)/93)^2)/108.9)^2 = 1
we can first simplify the equation by multiplying through by the denominators and then isolate the square root term:
((x-225)/250)^2 + (93^2*(1-((x-1.5)/93)^2)/108.9^2) = 1
((x-225)/250)^2 + 93^2*(1-((x-1.5)/93)^2)/(108.9^2) = 1
Now, let's solve for x by isolating the terms with x:
((x-225)/250)^2 = 1 - 93^2*(1-((x-1.5)/93)^2)/(108.9^2)
((x-225)/250)^2 = 1 - (93^2/108.9^2)*(1-((x-1.5)/93)^2)
Now, we can solve for x, let's take the square root of both sides:
x-225)/250 = ± sqrt(1 - (93^2/108.9^2)*(1-((x-1.5)/93)^2))
(x-225)/250 = ± sqrt(1 - (93^2/108.9^2)*(1-((x-1.5)/93)^2))
Then, solve for x by isolating it:
x-225 = 250* ± sqrt(1 - (93^2/108.9^2)*(1-((x-1.5)/93)^2))
Finally, solve for x:
x = 225 + 250* ± sqrt(1 - (93^2/108.9^2)*(1-((x-1.5)/93)^2))
Unfortunately, this equation doesn't have a simple closed-form solution for x. If you have specific values for the constants, you can use numerical methods or a graphing calculator to find the approximate solutions.
