Re:Re:Re:Topic 5 DQ 1

how to solve 4x2  + 4x - 1 =0

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You can use the quadratic formula: x=(-4+sqrt(16+16))/8 (the formula is x=(-b+sqrt(b^2-4ac))/2a, where a=4, b=4 and c=-1). From this x=(-4+sqrt(32))/8=(-4+4sqrt(2))/8=(-1+sqrt(2))/2=(-1+1.414)/2=0.207 or -1.207 approx.

Another approach is to complete the square: 4x^2+4x-1=4x^2+4x+1-2=0, which is (2x+1)^2=2, so 2x+1=+sqrt(2). Thus 2x=sqrt(2)-1=0.414 or 2x=-sqrt(2)-1=-2.414. So x=0.207 or -1.207.

by Top Rated User (1.2m points)

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