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solve a perfect square trinomial equation.

(4x+1)(x+4)=49

Rewrite it by multiplying it out, and factor.
4x^2 + 17x -45 = 0.
I don't see any "perfect square" here.
It also does not factor easily. Use the quadratic equation.
x = [-17 +/- sqrt(1009)]/8

x = 1.846 is one of the two solutions

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