Quadratic equations by facotring
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Quadratic equations by facotring

[From: ] [author: ] [Date: 12-05-30] [Hit: ]
(t-1)(t-5)=0Set each of the factors of the left-hand side of the equation equal to 0.t-1=0_t-5=0Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.t=1_t-5=0Set each of the factors of the left-hand side of the equation equal to 0.t=1_t-5=0Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides.......
b=-2_2b-3=0

Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
b=-2_2b=3

Divide each term in the equation by 2.
b=-2_b=(3)/(2)

The complete solution is the set of the individual solutions.
b=-2,(3)/(2)
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3t^(2)-18t+15=0

Factor out the GCF of 3 from 3t^(2)-18t+15.
3(t^(2)-6t+5)=0

Factor the trinomial t^(2)-6t+5.
3(t-1)(t-5)=0

Divide both sides of the equation by 3. Dividing 0 by any non-zero number is 0.
(t-1)(t-5)=0

Set each of the factors of the left-hand side of the equation equal to 0.
t-1=0_t-5=0

Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.
t=1_t-5=0

Set each of the factors of the left-hand side of the equation equal to 0.
t=1_t-5=0

Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides.
t=1_t=5

The complete solution is the set of the individual solutions.
t=1,5
------------------------
2x^(2)+3x-2=0

Find the factors such that the product of the factors is the trinomial 2x^(2)+3x-2. This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
(x+2)(2x-1)=0

Set each of the factors of the left-hand side of the equation equal to 0.
x+2=0_2x-1=0

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2_2x-1=0

Set each of the factors of the left-hand side of the equation equal to 0.
x=-2_2x-1=0

Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.
x=-2_2x=1

Divide each term in the equation by 2.
x=-2_x=(1)/(2)

The complete solution is the set of the individual solutions.
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