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Solve for x. {:[x^(2)+12 x+36=0],[x=]:}

Solve for x x .\newlinex2+12x+36=0x=□ \begin{array}{l} x^{2}+12 x+36=0 \\ x=\square \end{array}

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Q. Solve for x x .\newlinex2+12x+36=0x=□ \begin{array}{l} x^{2}+12 x+36=0 \\ x=\square \end{array}
  1. Identify quadratic equation: Identify the quadratic equation to solve.\newlineWe have the quadratic equation x2+12x+36=0x^2 + 12x + 36 = 0.
  2. Factor the equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 3636 and add up to 1212. The numbers 66 and 66 satisfy these conditions because 6×6=366 \times 6 = 36 and 6+6=126 + 6 = 12.\newlineSo, we can write the equation as (x+6)(x+6)=0(x + 6)(x + 6) = 0.
  3. Solve for x: Set each factor equal to zero and solve for x.\newlineFirst factor: x+6=0x + 6 = 0\newlineSubtract 66 from both sides to solve for x: x=−6x = -6\newlineSecond factor: Since it is the same as the first factor, it will give the same solution for x.
  4. Write the solutions: Write the solutions for the equation x2+12x+36=0x^2 + 12x + 36 = 0.\newlineThe solutions are x=−6x = -6, −6-6, but since they are the same, we can simply say x=−6x = -6.

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