6.9*10^-13=((2x)^2/(1-x)(2-2x)^2 solve for x
To solve the equation (6.9*10^-13) = ((2x)^2 / ((1-x)*(2-2x)^2)) for x, we need to rearrange the equation and apply the rules of algebraic simplification. Here's the step-by-step solution:
Step 1: Distribute the denominator
(6.9*10^-13) = ((2x)^2 / (2-2x)^2*(1-x))
Step 2: Simplify the numerator
(6.9*10^-13) = (4x^2 / (2-2x)^2*(1-x))
Step 3: Multiply both sides by the denominator to remove it from the equation
(6.9*10^-13)*(2-2x)^2*(1-x) = 4x^2
Step 4: Expand the expression to eliminate the squares
(6.9*10^-13)*(4-8x+4x^2)*(1-x) = 4x^2
Step 5: Distribute and simplify the expression
(6.9*10^-13)*(4-8x+4x^2-4x+8x^2-4x^3) = 4x^2
Step 6: Multiply through by 10^13 to eliminate the decimal point
6.9*(4-8x+4x^2-4x+8x^2-4x^3) = 4x^2*10^13
Step 7: Simplify and rearrange the equation to polynomial form
27.6 - 55.2x + 27.6x^2 - 27.6x + 55.2x^2 - 27.6x^3 = 4x^2*10^13
Step 8: Combine like terms
27.6 - 82.8x + 82.8x^2 - 27.6x^3 = 4x^2*10^13
Step 9: Move all the terms to the left-hand side
27.6 - 82.8x + 82.8x^2 - 27.6x^3 - 4x^2*10^13 = 0
Step 10: In order to find the solutions for x, you can use numerical methods such as graphing or using a calculator with a "solve" function.