How do you factor #2x^2+5x-30#?

1 Answer
George C.
May 26, 2016

#2x^2+5x-30 = 1/8(4x+5-sqrt(265))(4x+5+sqrt(265))#

Explanation:

Complete the square, first premultiplying by #8# to cut down on fraction arithmetic, not forgetting to divide by #8# at the end:

#8(2x^2+5x-30)#

#=16x^2+40x-240#

#=(4x)^2+2(4x)(5)-240#

#=(4x+5)^2-25-240#

#=(4x+5)^2-265#

#=(4x+5)^2-(sqrt(265)^2)#

#=((4x+5)-sqrt(265))((4x+5)+sqrt(265))#

#=(4x+5-sqrt(265))(4x+5+sqrt(265))#

Dividing both ends by #8#, we find:

#2x^2+5x-30 = 1/8(4x+5-sqrt(265))(4x+5+sqrt(265))#

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