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20 May, 04:57

4x^ (2) = 13x-3 use quadratic formula

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  1. 20 May, 05:23
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    The quadratic formula is - b + / - sqrt (b^2-4ac) all over 2a.

    First we have to get all the variables on one side so ... Subtract 4x: 0=-4x^ (2) + 13x-3

    OR add 3 and subtract 13x: 4x^ (2) - 13x+3=0

    Since I prefer a to be positive, I'm going to choose the second equation.

    So ... now we just plug and chug. a is the value of the variable squared. In this case a=4. b is the value with the variable, or b=-13. c is the last term. c=3

    **Remember: Ax^ (2) + By+C**

    Now we just plug everything in.

    -b = 13 (negative minus a negative is a positive)

    +/-sqrt ((-13) ^ (2) - 4 (4) (3))

    all over 2 (4)

    So work with the radical first.

    (-13) ^2=169

    4 (4) (3) = 48

    +/-sqrt (169-48)

    +-sqrt (121)

    sqrt (121) = 11

    Now it's just: (13+/-11) / 2 (4)

    (13+/-11) / 8

    Split this into two equations:

    (13+11) / 8

    (13-11) / 8

    Solve both: 24/8=3

    2/8=1/4

    So x = 3, 1/4

    Plug them back in and see if there's one solution or two:

    4 (3) ^2=13 (3) - 3

    36=36

    So x=3.

    How about 1/4?:

    4 (1/4) ^2=13 (1/4) - 3

    4 (1/16) = 13/4-3

    4/16=13/4-3

    1/4=13/4-3

    1/4=13/4 - (3x4) / (1x4) * Like denominators to add or subtract*

    1/4=13/4-12/4

    1/4=1/4.

    So x=1/4.

    In this case, both answers work. So the answer, using the quadratic formula is x=1/4, x=3
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