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Find one value of x that is a solution to the equation: {:[(3x+5)^(2)+5(3x+5)+6=0],[x=◻]:}

Find one value of x x that is a solution to the equation:\newline(3x+5)2+5(3x+5)+6=0x=□ \begin{array}{l} (3 x+5)^{2}+5(3 x+5)+6=0 \\ x=\square \end{array}

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Solve a quadratic equation by factoringright chevron icon

Full solution

Q. Find one value of x x that is a solution to the equation:\newline(3x+5)2+5(3x+5)+6=0x=□ \begin{array}{l} (3 x+5)^{2}+5(3 x+5)+6=0 \\ x=\square \end{array}
  1. Simplifying the equation: Let's first simplify the given equation by expanding the square and distributing the multiplication.\newline(3x+5)2+5(3x+5)+6=0(3x+5)^2 + 5(3x+5) + 6 = 0\newlineExpanding the square:\newline(3x+5)(3x+5)+5(3x+5)+6=0(3x+5)(3x+5) + 5(3x+5) + 6 = 0\newline9x2+15x+15x+25+15x+25+6=09x^2 + 15x + 15x + 25 + 15x + 25 + 6 = 0\newlineCombine like terms:\newline9x2+45x+56=09x^2 + 45x + 56 = 0
  2. Expanding the square: Now we need to factor the quadratic equation 9x2+45x+56=09x^2 + 45x + 56 = 0.\newlineWe are looking for two numbers that multiply to 9×569 \times 56 and add up to 4545.\newlineThe numbers 99 and 5656 have a product of 504504, so we need two factors of 504504 that add up to 4545.\newlineAfter some trial and error, we find that 99 and 5656 are the factors we need.\newlineSo we can write the equation as:\newline9×569 \times 5600

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