how to solve this:
((x^2)/(275625)) + ((78400)/(122500)) = 1
i tried again and i solved it.
If your solution x=315 you solve it correctly.
To solve the equation:
((x^2)/(275625)) + ((78400)/(122500)) = 1,
you can follow these steps:
Step 1: Simplify the fractions on the left side of the equation:
In the first fraction, the denominator is not a perfect square, so we leave it as it is.
In the second fraction, both the numerator and denominator are perfect squares. Hence, we simplify the fraction to get (56^2)/(35^2).
The equation now becomes:
(x^2)/(275625) + (56^2)/(35^2) = 1
Step 2: Find a common denominator for the fractions on the left side:
The common denominator for the fractions is the product of both denominators. In this case, the common denominator is (275625) * (35^2).
Step 3: Rewrite the fractions with the common denominator:
Multiply both the numerator and denominator of each fraction by the appropriate factor to make the denominators equal to the common denominator:
[(x^2) * (35^2) + (56^2) * (275625)] / [(275625) * (35^2)] = 1
Step 4: Combine the numerators:
Multiply the numerator and denominator of each fraction and then combine the resulting numerators:
[(x^2) * (35^2) + (56^2) * (275625)] = (275625) * (35^2)
Step 5: Simplify the equation:
Compute the values on each side of the equation:
(x^2) * (1225) + (56^2) * (275625) = (275625) * (1225)
Step 6: Solve for x:
Bring all terms involving x to one side of the equation and constants to the other side:
(x^2) * (1225) = (275625) * (1225) - (56^2) * (275625)
Step 7: Simplify the equation:
Compute the values on the right-hand side of the equation:
(x^2) * (1225) = (275625 - 56^2) * (1225)
Step 8: Solve for x:
Divide both sides of the equation by (1225) to isolate x:
x^2 = [(275625 - 56^2) * (1225)] / (1225)
Step 9: Take the square root of both sides:
Take the square root of both sides of the equation to solve for x:
x = ±√{[(275625 - 56^2) * (1225)] / (1225)}
Now, you can simplify the expression further and evaluate the square root to find the solutions for x.