solve by factoring 4x^2-8x+4=0 must show work
- print Print
- list Cite
Expert Answers
calendarEducator since 2006
write192 answers
starTop subjects are Science, Math, and Literature
4x^2-8x+4=0 by factoring
Factor out the GCF of 4 from each term in the polynomial.
4(x^2) + 4(-2x) + 4(1) =0
4 (x^2-2x+1)=0
4 (x-1) (x-1) =0
Combine the two common factors of (x-1) by adding the exponents.
4 (x-1)^2 =0
Divide both sides of the equation by 4 which leaves
(x-1)^2 = 0
Set each factor equal to 0
x-1 = 0
Add 1 to each side to solve for x
x=1
Related Questions
- `4x^2- 8x + 4 = 0` Solve by factoring
- 2 Educator Answers
- Solve for sqrt(x^2 - 4x +4) =0
- 1 Educator Answer
- Solve by factoring: 3x^2 + 5x - 2 = 0.Solve by factoring. 1. x^2 + 5x + 6 = 0 2. 2x^2 - x - 3 =...
- 2 Educator Answers
- solve x : x^4 -4x^2 -32 = 0
- 2 Educator Answers
- Please solve x^2 + 6x - 7 = 0. Please show your work.
- 1 Educator Answer
The equation 4x^2-8x+4=0 has to be solved.
4x^2-8x+4=0
Factor the number 4 that is common to all the terms.
4(x^2 - 2x + 1) = 0
Now write -2 as a sum of two numbers t1 and t2 such that their sum t1 + t2 = -2 and the product t1*t2 = 1*1 = 1
-2 can be written as the sum of -1 and -1. This gives:
4*(x^2 - x - x + 1) = 0
4*(x(x - 1) - 1(x - 1)) = 0
4*(x - 1)(x - 1) = 0
x - 1 = 0
x = 1
The solution of the equation 4x^2-8x+4=0 is x = 1
Student Answers