Answer:
The equation 36x^2 + 61x + 20 = 0 solves to x = -4/9 or x = -5/4
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Step-by-step explanation:
x = -4/9 or x = -5/4 .... given solutions
9x = -4 or 4x = -5 .... multiply both sides by denominator
9x+4 = 0 or 4x+5 = 0 .... get everything to one side
(9x+4)(4x+5) = 0 .... zero product property
y(4x+5) = 0 ...... let y = 9x+4
y*4x + y*5 = 0 .... distribute
4xy + 5y = 0
4x( y ) + 5( y ) = 0
4x( 9x+4) + 5( 9x+4 ) = 0 ... plug in y = 9x+4
4x*9x + 4x*4 + 5*9x + 5*4 = 0 ..... distribute
36x^2 + 16x + 45x + 20 = 0
36x^2 + 61x + 20 = 0
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The equation 36x^2 + 61x + 20 = 0 has the two solutions x = -4/9 and x = -5/4
We can use the quadratic formula to confirm this.