-4x²-3x+1 = 0
Make the leading term positive by multiplying by -1
4x²+3x-1 = 0
Get the -1 off the left side by adding 1 to both sides:
4x²+3x = 1
Divide every number through by 4
x²+x =
x²+x =
1. Multiply the coefficient of x, by , getting
2. Square , getting =
3. Add to both sides:
x²+x+ = +
The left side will now factor
as a square: x²+x+ = (x+)(x+) = (x+)²
Combine the fractions on the right by getting a LCD of 64: + = + =
(x+)² =
take square roots of both sides:
(x+) =
Add } to both sides:
x =
Using the + : x = = =
Using the - : x = = = -1
Solutions: and -1
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It could have been done by factoring:
-4x²-3x+1 = 0
Make the leading term positive by multiplying by -1
4x²+3x-1 = 0
(4x-1)(x+1) = 0
4x-1 = 0; x+1 = 0
4x = 1 x = -1
x =
Edwin
