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10 January, 01:31

What is the quadratic portion in this quadratic equation 7x2-12x+16=0

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  1. 10 January, 01:47
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    x = 6/7 + (2 i sqrt (19)) / 7 or x = 6/7 - (2 i sqrt (19)) / 7

    Step-by-step explanation:

    Solve for x:

    7 x^2 - 12 x + 16 = 0

    Hint: | Write the quadratic equation in standard form.

    Divide both sides by 7:

    x^2 - (12 x) / 7 + 16/7 = 0

    Hint: | Solve the quadratic equation by completing the square.

    Subtract 16/7 from both sides:

    x^2 - (12 x) / 7 = - 16/7

    Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

    Add 36/49 to both sides:

    x^2 - (12 x) / 7 + 36/49 = - 76/49

    Hint: | Factor the left hand side.

    Write the left hand side as a square:

    (x - 6/7) ^2 = - 76/49

    Hint: | Eliminate the exponent on the left hand side.

    Take the square root of both sides:

    x - 6/7 = (2 i sqrt (19)) / 7 or x - 6/7 = - (2 i sqrt (19)) / 7

    Hint: | Look at the first equation: Solve for x.

    Add 6/7 to both sides:

    x = 6/7 + (2 i sqrt (19)) / 7 or x - 6/7 = - (2 i sqrt (19)) / 7

    Hint: | Look at the second equation: Solve for x.

    Add 6/7 to both sides:

    Answer: x = 6/7 + (2 i sqrt (19)) / 7 or x = 6/7 - (2 i sqrt (19)) / 7
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