How do you solve factor # 2x^2 +4x-1 = 7x^2 - 7x +1#?

1 Answer
Jim G.
Mar 15, 2018

#x=1/5" or "x=2#

Explanation:

#"Rearrange into "color(blue)"standard form"#

#•color(white)(x)ax^2+bx+c=0color(white)(x);a!=0#

#2x^2+4x-1=7x^2-7x+1#

#rArr5x^2-11x+2=0larrcolor(blue)"in standard form"#

#"using the a-c method of factorising"#

#"the factors of + 10 which sum to - 11 are - 10 and - 1"#

#rArr5x^2-10x-x+2=0larrcolor(blue)"split the middle term"#

#rArrcolor(red)(5x)(x-2)color(red)(-1)(x-2)=0larrcolor(blue)"factor by grouping"#

#rArr(x-2)(color(red)(5x-1))=0#

#"equate each factor to zero and solve for x"#

#x-2=0rArrx=2#

#5x-1=0rArrx=1/5#

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