How do you solve #12 = 2x^2 - 5x#?

1 Answer
Mar 29, 2018

Answer:

#x=-3/2" or "x=4#

Explanation:

#"rearrange the equation into "color(blue)"standard form"#

#rArr2x^2-5x-12=0larrcolor(blue)"in standard form"#

#"factorise using the a-c method"#

#"that is factors of the product "2xx-12=-24#
#"which sum to - 5"#

#"the factors required are - 8 and + 3"#

#"'split' the middle term using these factors"#

#rArr2x^2-8x+3x-12=0larrcolor(blue)"factor by grouping"#

#rArrcolor(red)(2x)(x-4)color(red)(+3)(x-4)=0#

#"take out the common factor "(x-4)#

#rArr(x-4)(color(red)(2x+3))=0#

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

#x-4=0rArrx=4#

#2x+3=0rArrx=-3/2#