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28 August, 07:54

2x2 + 14x - 4 = - x2 + 3x

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Answers (1)
  1. 28 August, 08:32
    0
    first, lets solve by factoring:

    Let's solve your equation step-by-step.

    2x2+14x-4=-x2+3x

    Step 1: Subtract - x^2+3x from both sides.

    2x2+14x-4 - (-x2+3x) = -x2+3x - (-x2+3x)

    3x2+11x-4=0

    Step 2: Factor left side of equation.

    (3x-1) (x+4) = 0

    Step 3: Set factors equal to 0.

    3x-1=0 or x+4=0

    x=

    1

    3

    or x=-4

    we can also solve using the quadratic formula:

    2x2+14x-4=-x2+3x

    Step 1: Subtract - x^2+3x from both sides.

    2x2+14x-4 - (-x2+3x) = -x2+3x - (-x2+3x)

    3x2+11x-4=0

    Step 2: Use quadratic formula with a=3, b=11, c=-4.

    x=

    -b±√b2-4ac

    2a

    x=

    - (11) ±√ (11) 2-4 (3) (-4)

    2 (3)

    x=

    -11±√169

    6

    x=

    1

    3

    or x=-4

    lastly, we can complete the square.

    2x2+14x-4=-x2+3x

    Step 1: Add x^2 to both sides.

    2x2+14x-4+x2=-x2+3x+x2

    3x2+14x-4=3x

    Step 2: Subtract 3x from both sides.

    3x2+14x-4-3x=3x-3x

    3x2+11x-4=0

    Step 3: Add 4 to both sides.

    3x2+11x-4+4=0+4

    3x2+11x=4

    Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.

    3x2+11x

    3

    =

    4

    3

    x2+

    11

    3

    x=

    4

    3

    Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.

    Then we need to add (b/2) ^2=121/36 to both sides to complete the square.

    Add 121/36 to both sides.

    x2+

    11

    3

    x+

    121

    36

    =

    4

    3

    +

    121

    36

    x2+

    11

    3

    x+

    121

    36

    =

    169

    36

    Step 6: Factor left side.

    (x+

    11

    6

    ) 2=

    169

    36

    Step 7: Take square root.

    x+

    11

    6

    =±√

    169

    36

    Step 8: Add (-11) / 6 to both sides.

    x+

    11

    6

    +

    -11

    6

    =

    -11

    6

    ±√

    169

    36

    x=

    -11

    6

    ±√

    169

    36

    x=

    1

    3

    or x=-4

    Answer:

    x=

    1

    3

    or x=-4
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