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Solve for x. {:[x^(2)-18 x+81=0],[x=]:}

Solve for x x .\newlinex2−18x+81=0x=□ \begin{array}{l} x^{2}-18 x+81=0 \\ x=\square \end{array}

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Q. Solve for x x .\newlinex2−18x+81=0x=□ \begin{array}{l} x^{2}-18 x+81=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation.\newlineThe given quadratic equation is x2−18x+81=0x^2 - 18x + 81 = 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 8181 (the constant term) and add up to −18-18 (the coefficient of the xx term). The numbers that satisfy these conditions are −9-9 and −9-9, since (−9)×(−9)=81(-9) \times (-9) = 81 and (−9)+(−9)=−18(-9) + (-9) = -18.
  3. Write the factored form: Write the factored form of the equation.\newlineUsing the numbers found in Step 22, we can write the factored form of the equation as (x−9)(x−9)=0(x - 9)(x - 9) = 0.
  4. Solve for x using the factored form: Solve for x using the factored form.\newlineSet each factor equal to zero and solve for x:\newlinex−9=0x - 9 = 0\newlineAdd 99 to both sides:\newlinex−9+9=0+9x - 9 + 9 = 0 + 9\newlinex=9x = 9\newlineSince both factors are the same, we only get one unique solution for xx.

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