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Solve for x. {:[3x^(2)+18 x+27=0],[x=◻]:}

Solve for x x .\newline3x2+18x+27=0x=□ \begin{array}{l} 3 x^{2}+18 x+27=0 \\ x=\square \end{array}

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Full solution

Q. Solve for x x .\newline3x2+18x+27=0x=□ \begin{array}{l} 3 x^{2}+18 x+27=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to solve.\newlineThe given quadratic equation is 3x2+18x+27=03x^2 + 18x + 27 = 0.
  2. Factor out the greatest common factor: Factor out the greatest common factor (GCF) if possible.\newlineThe GCF of the coefficients 33, 1818, and 2727 is 33. We can factor out 33 from each term.\newline3(x2+6x+9)=03(x^2 + 6x + 9) = 0
  3. Solve the factored quadratic equation: Solve the factored quadratic equation.\newlineNow we have the equation in the form 3(a2+2ab+b2)=03(a^2 + 2ab + b^2) = 0, which is a perfect square trinomial.\newline(x+3)2=0(x + 3)^2 = 0
  4. Find the value of x: Find the value of x.\newlineSince (x+3)2=0(x + 3)^2 = 0, we can take the square root of both sides to solve for x.\newlinex+3=0x + 3 = 0\newlineSubtract 33 from both sides to isolate x.\newlinex=−3x = -3

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