Question

Select the two values of x that are roots of this equation

2x - 3 = -5x^2

A. x = 3/5
B. x = - 1
C. x = 5/3
D. x = - 2/3

Answer 1

`\sf 2x - 3 = -5x^2`

move terms to one side:

`\sf 2x - 3 = -5x^2=0`

Split second term in 2x-3+5x^2 into two terms:

`\sf 5x^2+5x-3x-3=0`

factor out common terms in first terms, then last terms

`\sf 5x(x+1)-3(x+1)=0`

Factor out common term: x+1

`(x+1)(5x-3)=0`

solve for x

`\sf x+1=0`

• 
  `\sf x+1-1=0-1`

• 
  `\boxed{\sf x=-1}`

`\sf 5x-3=0`

• 
  `\sf 5x-3+3=0+3`

• 
  `\sf 5x=3`

• 
  `\sf \cfrac{5x}{5}=\cfrac{3}{5}`

• 
  `\boxed{\sf x=(3)/(5)}`

`\boxed{\sf Answer: x=-1,\:x=(3)/(5)}`