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Solve for xx.\newline19x2+36x=019x^2 + 36x = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinex=x = ____

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Q. Solve for xx.\newline19x2+36x=019x^2 + 36x = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinex=x = ____
  1. Factor GCF and Factorize: Factor out the greatest common factor (GCF). The GCF of 19x219x^2 and 36x36x is xx. Factor out xx from each term in the equation 19x2+36x=019x^2 + 36x = 0. x(19x+36)=0x(19x + 36) = 0
  2. Apply Zero-Product Property: Apply the zero-product property.\newlineFor the product of factors to be zero, at least one of the factors must be zero.\newlineTherefore, we set each factor equal to zero and solve for xx.\newlinex=0x = 0 and 19x+36=019x + 36 = 0
  3. Solve for x: Solve the second equation for x.\newlineSubtract 3636 from both sides of the equation 19x+36=019x + 36 = 0.\newline19x+36−36=0−3619x + 36 - 36 = 0 - 36\newline19x=−3619x = -36\newlineDivide both sides by 1919 to isolate xx.\newlinex=−3619x = -\frac{36}{19}
  4. Write Solutions: Write the values of xx. We found two solutions: x=0x = 0 and x=−3619x = -\frac{36}{19}. x=0,−3619x = 0, -\frac{36}{19}

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