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Find one value of x that is a solution to the equation: {:[(4x+1)^(2)+9(4x+1)=-18],[x=◻]:}

Find one value of x x that is a solution to the equation:\newline(4x+1)2+9(4x+1)=−18x=□ \begin{array}{l} (4 x+1)^{2}+9(4 x+1)=-18 \\ x=\square \end{array}

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Q. Find one value of x x that is a solution to the equation:\newline(4x+1)2+9(4x+1)=−18x=□ \begin{array}{l} (4 x+1)^{2}+9(4 x+1)=-18 \\ x=\square \end{array}
  1. Simplify the equation: Simplify the equation.\newlineWe need to simplify the equation (4x+1)2+9(4x+1)=−18(4x+1)^2 + 9(4x+1) = -18 by expanding the square and distributing the 99.\newline(4x+1)(4x+1)+9(4x+1)=−18(4x+1)(4x+1) + 9(4x+1) = -18\newline16x2+4x+4x+1+36x+9=−1816x^2 + 4x + 4x + 1 + 36x + 9 = -18\newlineCombine like terms.\newline16x2+44x+10=−1816x^2 + 44x + 10 = -18
  2. Combine like terms: Move all terms to one side to set the equation to zero.\newlineSubtract 1010 from both sides to get all terms on one side.\newline16x2+44x+10−10=−18−1016x^2 + 44x + 10 - 10 = -18 - 10\newline16x2+44x=−2816x^2 + 44x = -28
  3. Move all terms to one side: Factor the quadratic equation.\newlineWe need to factor the quadratic equation 16x2+44x+28=016x^2 + 44x + 28 = 0. However, we made a mistake in the previous step; we should have subtracted 1010 from both sides, but we incorrectly added 2828 instead of subtracting 1010. Let's correct this.\newline16x2+44x+10=−1816x^2 + 44x + 10 = -18\newline16x2+44x+10+18=−18+1816x^2 + 44x + 10 + 18 = -18 + 18\newline16x2+44x+28=016x^2 + 44x + 28 = 0\newlineNow we can proceed to factor the equation.

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