What are the solutions of 3x² + 14x + 16 = 0?

Given: A quadratic equation: 3x² + 14x + 16 = 0

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 the coefficient of x² = 3, b is the coefficient of x = 14, and c is the constant term = 16.

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

3 × ( 16) = 48

⇒ 8 and 6 are the factors that add up to b.

Step 3: Split bx into two terms.

3x² + 6x + 8x + 16 = 0

Step 4: Take out the common factors by grouping.

3x (x + 2) + 8 (x + 2) = 0

(3x + 8 ) (x + 2) = 0

Step 5: By putting the factors equal to zero we get two values of x

3x + 8 = 0 and x + 2 = 0

x = - 8 / 3 and x = - 2

Thus, the two values that satisfy the equation are - 8/3 and - 2.

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What are the solutions of 3x² + 14x + 16 = 0?

Summary:

The solutions of the equation 3x² + 14x + 16 = 0 are - 8/3 and -2 which satisfies the equation.