Blake knows that one of the solutions to x² - 6x + 8 = 0 is x = 2. What is the other solution?

Solution:

Let us factorize the quadratic equation to find the value of x by splitting the middle term.

Step 1: Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 1, b is the coefficient of x = -6 and c is the constant term = 8.

Step 2: Multiply a and c and find the factors that add up to b.

1 × (8) = 8

⇒ -2 and -4 are the factors that add up to b.

Step 3: Split bx into two terms.

x² - 2x - 4x + 8 = 0

Step 4: Take out the common factors by grouping.

x (x - 2) - 4(x - 2) = 0

(x - 2)(x - 4) = 0

By putting the factors equal to zero we get two values of x

x - 2 = 0 and x - 4 = 0

x = 2 and x = 4

Thus, the two values that satisfy the equation are 4 and 2.

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Blake knows that one of the solutions to x² - 6x + 8 = 0 is x = 2. What is the other solution?

Summary:

The other solution to the equation x² - 6x + 8 = 0 is x = 4