Question 778861
<pre>

-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

{{{4/4}}}x²+{{{3/4}}}x = {{{1/4}}}

x²+{{{3/4}}}x = {{{1/4}}}

1. Multiply the coefficient  of x, {{{3/4}}} by {{{1/2}}}, getting {{{3/8}}}
2. Square {{{3/8}}}, getting {{{(3/8)^2}}} = {{{9/64}}}
3. Add {{{9/64}}} to both sides:

x²+{{{3/4}}}x+{{{9/64}}} = {{{1/4}}}+{{{9/64}}}

The left side will now factor 
as a square: x²+{{{3/4}}}x+{{{9/64}}} = (x+{{{3/8}}})(x+{{{3/8}}}) = (x+{{{3/8}}})²
Combine the fractions on the right by getting a LCD of 64: {{{1/4}}}+{{{9/64}}} = {{{16/64}}}+{{{9/64}}} = {{{25/64}}}

(x+{{{3/8}}})² = {{{25/64}}}

take square roots of both sides:

{{{sqrt((x+3/8)^2)}}}{{{""=""}}}{{{"" +- sqrt(25/64)}}}

(x+{{{3/8}}}) = {{{"" +- 5/8}}}

Add {{{-3/8}}}} to both sides:

x = {{{-3/8 +- 5/8}}}

Using the + :  x = {{{-3/8 + 5/8}}} = {{{2/8}}} = {{{1/4}}}

Using the - :  x = {{{-3/8 - 5/8}}} = {{{(-8)/8}}} = -1

Solutions: {{{1/4}}} 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 = {{{1/4}}}

Edwin</pre>