(a) 18x + 5 = -9x^2

(b) 4x^2 + 10x + 3 = 0

(c) 3x^2 + 4x + 7 = 0

(d) 4x(x+3) - 2(x-2) = -3x^2 + 15 = - 2x
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1 Answer

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(a) 9x²+18x=-5, 9x²+18x+5=0=(3x+5)(3x+1), x=-5/3 or -1/3.

(b) 4x²+10x+3=0,

x²+5x/2=-3/4,

x²+5x/2+25/16=25/16-3/4=13/16,

(x+5/4)²=13/16,

x+5/4=±√13/4,

x=-5/4+√13/4 or -5/4-√13/4.

(c) 3x²+4x+7=0,

x²+4x/3=-7/3,

x²+4x/3+4/9=4/9-7/3=-17/9,

(x+2/3)²=-17/9 for which there are only complex solutions:

x=-2/3±i√17/3.

(d) 4x²+12x-2x+4=-3x²+15=-2x.

Three equations are implied:

(i) 7x²+10x-11=0,

x=(-10±√(100+308))/14=(-10±2√102)/14.

(ii) 3x²-2x-15=0,

x=(2±√(4+180))/6=(1±√46)/3.

(iii) 4x²+12x+4=0=4(x²+3x+1),

x=(-3±√5)/2.

The “solutions” are inconsistent so there is no solution.

by Top Rated User (815k points)

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