alg II

how do you solve this equation

2 cos pi x = 4x + 5

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  1. Using a calculator set to radians, the old-fashioned trial-and-error method might work.
    first I made a sketch of
    y = 2cos πx and y = 4x+5 and noticed that there is one solution and x is negative

    let f(x) = 2cosπx - 4x - 5
    f(-1) = -.0015 , very close
    f(-1.1) = +.39
    f(-1.05) = .198
    f(-1.025) = 0.984
    f(-1.02) =.078
    f(-1.01) = .0185
    f(-1.0025) = .0085
    f(-1.00125) = etc.

    There is no simple arithmetic way to do this.
    If you know Calculus, you might want to try Newton's Method

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