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Solve for x. {:[x^(2)+6x+9=0],[x=◻]:}

Solve for x x .\newlinex2+6x+9=0x=□ \begin{array}{l} x^{2}+6 x+9=0 \\ x=\square \end{array}

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Q. Solve for x x .\newlinex2+6x+9=0x=□ \begin{array}{l} x^{2}+6 x+9=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to solve.\newlineThe given quadratic equation is x2+6x+9=0x^2 + 6x + 9 = 0. We need to find the values of xx that satisfy this equation.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 99 (the constant term) and add up to 66 (the coefficient of xx). The numbers 33 and 33 satisfy these conditions because 3×3=93 \times 3 = 9 and 3+3=63 + 3 = 6.\newlineSo, we can write the equation as (x+3)(x+3)=0(x + 3)(x + 3) = 0.
  3. Set each factor equal to zero: Set each factor equal to zero and solve for xx.\newlineSince (x+3)(x+3)=0(x + 3)(x + 3) = 0, we can set each factor equal to zero to find the solutions for xx.\newlinex+3=0x + 3 = 0\newlineSubtract 33 from both sides to solve for xx.\newlinex=−3x = -3
  4. Check for additional solutions: Check for additional solutions.\newlineSince both factors are the same, (x+3)(x + 3), we only have one unique solution for this equation.\newlinex=−3x = -3

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