factor the high- degree polynomial expression of 7x^2+42x +63=0 and then solve for the value of x x=

Answer 1

First, we can factor the polynomial expression \(7x^2 + 42x + 63 = 0\).

1. Factor out the greatest common factor:
   The coefficients \(7\), \(42\), and \(63\) have a common factor of \(7\). So, we can factor out \(7\): \[ 7(x^2 + 6x + 9) = 0 \]

2. Factor the quadratic expression \(x^2 + 6x + 9\):
   The expression can be factored as follows: \[ x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2 \]

3. Combine the factored terms:
   Therefore, we can write the equation as: \[ 7(x + 3)^2 = 0 \]

4. Set the factors equal to zero:
   Since \(7\) is not equal to zero, we can focus on: \[ (x + 3)^2 = 0 \]

5. Solve for \(x\):
   Taking the square root on both sides: \[ x + 3 = 0 \] Thus, solving for \(x\), we get: \[ x = -3 \]

Therefore, the solution for the value of \(x\) is: \[ \boxed{-3} \]