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Solve the following equations. Leave radicals in radical form(do not calculate there approximate values).
a.
Replace the middle term with two numbers that multiply to give you 4x^2*-10=-40x^2, but add to give you 3x. 8x*-5x=-40x^2, 8x+-5x=3x.
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Factor by grouping, group the first two terms and the last two.
Factor the GCF out of each parentheses
Factor out x+2
Set each parentheses equal to 0 and solve for x.
4x-5=0 and x+2=0
4x=5 and x=-2
4x/4=5/4 and x=-2
x=5/4 and x=-2
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b. 2x^2=3x Set equal to 0
Factor out the GCF.
x(2x-3)=0
x=0 and 2x-3=0
x=0 and 2x=3
x=0 and 2x/2=3/2
x=0 and x=3/2
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c. x^3-4x^2-x+4=0 Factor by grouping
x^2-1 is the difference of squares
(x+1)(x-1)(x-4)=0
x+1=0 and x-1=0 and x-4=0
x=-1 and x=1 and x=4
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d. x^4-10x^2+9=0
(x+3)(x-3)(x+1)(x-1)=0
x+3=0 and x-3=0 and x+1=0 and x-1=0
x=-3 and x=3 and x=-1 and x=1
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e. x^3-3x^2+x-3=0
(x^2+1 is prime, so if you need only real numbers you can ignore it, otherwise it's solution is +/-i)
x-3=0
x=3
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f. 3x^2-5x+1=0
a=3 b=-5 and c=1
The quadratic formula is
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An abreviation for radical is "sqrt(whatever you want)" like the square root of x+5 is sqrt(x+5)
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Happy Calculating!!!
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