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4 June, 01:18

What are the solutions to the quadratic equation x^2=7x+4

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  1. 4 June, 01:54
    0
    x = 7/2 ±sqrt (65) / 2

    Step-by-step explanation:

    x^2=7x+4

    Subtract 7x from each side

    x^2-7x=7x-7x+4

    x^2 - 7x = 4

    Complete the square

    Take the coefficient of x and divide by 2

    -7/2

    Then square it

    (-7/2) ^2 = 49/4

    Add this to each side

    x^2 - 7x + 49/4 = 4+49/4

    (x-7/2) ^2 = 4 + 49/4

    (x-7/2) ^2 = 16/4 + 49/4

    (x-7/2) ^2 = 65/4

    Take the square root of each side

    sqrt ((x-7/2) ^2) = ±sqrt (65/4)

    x-7/2 = ±sqrt (65) / sqrt (4)

    x-7/2 = ±sqrt (65) / 2

    Add 7/2 to each side

    x-7/2 + 7/2=7/2 ±sqrt (65) / 2

    x = 7/2 ±sqrt (65) / 2
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