SIMULTANEOUS EQUATION

Solve the equation 5x^2-5x-63=0 by using the "complete the square" method. Give your answer to 2 decimal place.

Please show me in clear steps how to get the answers 4.08 and -3.08.

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  1. 5x^2-5x-63
    = 5(x^2-x) - 63
    Recall that (x-a)^2 = a^2-2a+a^2
    Here we have 2a = 1, so a = 1/2. So, add and subtract 1/4 * 5

    = 5(x^2-x + 1/4) - 63 - 5/4
    = 5(x - 1/2)^2 - 267/4

    To get the roots, set that to zero:

    5(x - 1/2)^2 - 257/4 = 0
    5(x - 1/2)^2 = 257/4
    (x - 1/2)^2 = 257/20
    x - 1/2 = ±√(257/20)
    x = 1/2 ±√(257/20)
    x = -3.08 or 4.08

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  2. xy=90
    2x+y=36

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