Solve: x² − 5x+6=l5x + 6 = l don't know

Answer: x=2x = 2 or x=3x = 3

Step-by-step solution

Step 1: Identify the quadratic equation and method

We are given the standard quadratic equation x2−5x+6=0x^2 - 5x + 6 = 0. Here, the coefficients are a=1a = 1, b=−5b = -5, and c=6c = 6. We need to find two numbers whose sum is −5-5 and whose product is 1×6=61 \times 6 = 6.

Step 2: Split the middle term and factor

The numbers −2-2 and −3-3 satisfy (−2)+(−3)=−5(-2) + (-3) = -5 and (−2)(−3)=6(-2)(-3) = 6. We split the middle term −5x-5x into −2x−3x-2x - 3x, and factor by grouping common terms.

Step 3: Apply zero product property to find roots

Factoring out the common binomial (x−2)(x - 2) gives (x−2)(x−3)=0(x - 2)(x - 3) = 0. Setting each linear factor to 00, we obtain x−2=0  ⟹  x=2x - 2 = 0 \implies x = 2 and x−3=0  ⟹  x=3x - 3 = 0 \implies x = 3.

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