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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 the quadratic equation: Identify the quadratic equation to solve for xx.\newlineThe given equation is x2−12x+36=0x^2 - 12x + 36 = 0.\newlineWe need to find two numbers that multiply to 3636 and add up to −12-12.
  2. Find the two numbers: Find the two numbers that satisfy the conditions.\newlineThe numbers −6-6 and −6-6 multiply to 3636 and add up to −12-12.
  3. Write the factored form: Write the factored form of the quadratic equation using the numbers found.\newlineThe factored form is (x−6)(x−6)=0(x - 6)(x - 6) = 0.
  4. Set each factor equal to zero: Set each factor equal to zero and solve for xx.\ First, set x−6=0x - 6 = 0 and solve for xx.\ Adding 66 to both sides gives us x=6x = 6.
  5. Find the unique solution: Since both factors are the same, we only have one unique solution.\newlineThe solution is x=6x = 6.

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