how to solve for 6e-6/x2(squared)=2e-6/(4-x)2(squared)
To solve the equation (6e-6/x^2) = (2e-6/(4-x))^2, we can follow these steps:
Step 1: Simplify the right side of the equation.
Start by simplifying the right side of the equation by squaring (4-x) and multiplying it by 2e-6:
(2e-6/(4-x))^2 = (2e-6)^2/(4-x)^2
= (4e-12)/(16 - 8x + x^2) [using the exponent rule]
Step 2: Simplify the left side of the equation.
Now, let's simplify the left side of the equation:
6e-6/x^2 = 6e-6 * (1/x^2)
= 6e-6/x^2 [e-6 * 1 = e-6]
Step 3: Set the two sides equal to each other.
Now, we can set the simplified left side equal to the simplified right side:
6e-6/x^2 = (4e-12)/(16 - 8x + x^2)
Step 4: Cross-multiply and simplify.
To eliminate the fractions, we can cross-multiply:
6e-6 * (16 - 8x + x^2) = x^2 * (4e-12)
Expand and simplify the equation further:
96e-6 - 48e-6x + 6e-6x^2 = 4e-12x^2
Step 5: Combine like terms and move all terms to one side.
Combine like terms on both sides of the equation:
6e-6x^2 - 4e-12x^2 = 48e-6x - 96e-6
Simplify the equation further:
2e-6x^2 = 48e-6x - 96e-6
Step 6: Factor out common terms and set equal to zero.
Factor out common terms on the right side of the equation:
2e-6(x^2) = 48e-6(x - 2)
Now, let's set it equal to zero by moving the terms on the right side to the left side:
2e-6(x^2 - 24(x - 2)) = 0
Step 7: Solve for x.
To solve for x, we can set each factor equal to zero:
2e-6 = 0 [Not possible, as e-6 is a positive value]
x^2 - 24(x - 2) = 0
Now, you can solve the quadratic equation x^2 - 24(x - 2) = 0 using factoring, completing the square, or the quadratic formula.