How do you solve #x(1-x)+2x-4=8x-24-x^2#?

Question

Eva Adamson · Accepted Answer

See full process in the Explanation

First step is to expand the terms within the parenthesis: #x(1 - x) + 2x - 4 = 8x - 24 - x^2# #x - x^2 + 2x - 4 = 8x - 24 - x^2# We can now group and combine like terms: #x + 2x - x^2 - 4 = 8x - 24 - x^2# #3x - x^2 - 4 = 8x - 24 - x^2# We can now add and subtract the necessary terms to isolate the #x# terms while keeping the equation balanced: #3x - x^2 - 4 - color(red)(3x) + color(blue)(x^2) + color(green)(24) = 8x - 24 - x^2- color(red)(3x) + color(blue)(x^2) + color(green)(24)# #3x - color(red)(3x) - x^2 + color(blue)(x^2) - 4 + color(green)(24) = 8x - color(red)(3x) - 24 + color(green)(24) - x^2 + color(blue)(x^2)# #0 - 0 - 4 + color(green)(24) = 8x - color(red)(3x) - 0 - 0# #- 4 + color(green)(24) = 8x - color(red)(3x)# #20 = 5x# Now we can divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced: #20/color(red)(5) = (5x)/color(red)(5)# #4 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))# #4 = x# #x = 4#

Abigail Allen · Answer

undefined To solve the equation $x(1-x) + 2x - 4 = 8x - 24 - x^2$, follow these steps:

1. Expand and simplify both sides of the equation.
2. Combine like terms.
3. Rearrange the equation to set it to zero.
4. Identify the coefficients.
5. Apply the quadratic formula.
6. Solve for the values of $x$.