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x^(2)-12x+36=0 {:("Quantity A","Quanti...

`x^(2)-12x+36=0`
`{:("Quantity A","Quantity B"),(x,6):}`

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To solve the quadratic equation \( x^2 - 12x + 36 = 0 \) and compare Quantity A (x) and Quantity B (6), we can follow these steps: ### Step 1: Write the quadratic equation We start with the equation: \[ x^2 - 12x + 36 = 0 \] ### Step 2: Factor the quadratic equation We can factor the quadratic expression. Notice that: \[ x^2 - 12x + 36 = (x - 6)(x - 6) = (x - 6)^2 \] Thus, we can rewrite the equation as: \[ (x - 6)^2 = 0 \] ### Step 3: Solve for x To find the value of \( x \), we set the factored expression equal to zero: \[ x - 6 = 0 \] Solving for \( x \) gives: \[ x = 6 \] ### Step 4: Compare Quantity A and Quantity B Now we have: - Quantity A: \( x = 6 \) - Quantity B: \( 6 \) Since both quantities are equal, we conclude that: \[ \text{Quantity A} = \text{Quantity B} \] ### Final Conclusion Thus, the answer is that Quantity A is equal to Quantity B. ---
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