How do you solve for x in this problem? 4x^2 - 3 = -x?

3 Answers
May 12, 2018

x=-1" or "x=3/4

Explanation:

"rearrange into standard form "color(white)(x)ax^2+bx+c=0

"add "x" to both sides"

rArr4x^2+x-3=0larrcolor(blue)"in standard form"

"factor the quadratic using the a-c method"

"the factors of the product "4xx-3=-12

"which sum to + 1 are + 4 and - 3"

"split the middle term using these factors"

4x^2+4x-3x-3=0larrcolor(blue)"factor by grouping"

color(red)(4x)(x+1)color(red)(-3)(x+1)=0

"take out the "color(blue)"common factor "(x+1)

rArr(x+1)(color(red)(4x-3))=0

"equate each factor to zero and solve for x"

x+1=0rArrx=-1

4x-3=0rArrx=3/4

May 12, 2018

Explanation:

First we rearrange;

4x^2 -3 = -x
4x^2 +x-3=0

now we have ax^2 + bx + c =0 format, so we can use our quadratic equation to solve.

x = (-b+sqrt(b^2-4ac))/(2a)
and
x = (-b-sqrt(b^2-4ac))/(2a)
After subbing everything in we get x=-1 or x=.75

May 12, 2018

the answer
x=-1 and x=3/4

Explanation:

show below

4x^2 - 3 = -x

4x^2+x-3=0

(x+1)*(4x-3)=0

x+1=0 => x=-1

4x-3=0 => 4x=3 => x=3/4