Verified Answer :
Completing
the square is done as follows:
- Write the equation in a way that the constants are in the right side while
the terms with x are on the left.
- Make sure that the coefficient of the x^2 term is 1.
10(x^2 + 4x) = 13 - Adding a term to both sides that will complete the square in the left
side. This is done by dividing the coefficient of the x term by 2 and squaring
it. Note: The same amount should be added to the right side to balance the
equation.
10(x^2 + 4x + 4) =13 +40
10(x+2)^2 = 53
Therefore, the value of A is 10.
we have
\(10x^{2} + 40x - 13 = 0\)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(10x^{2} + 40x =13\)
Factor the leading coefficient
\(10(x^{2} + 4x) =13\) ----------> the value of A is \(10\)
Complete the square. Remember to balance the equation by adding the same constants to each side
\(10(x^{2} + 4x+4) =13+40\)
\(10(x^{2} + 4x+4) =53\)
Rewrite as perfect squares
\(10(x+2)^{2} =53\)
\(10(x+2)^{2} =53 \\ (x+2)^{2} =\frac{53}{10} \\ \\ x+2=(+/-)\sqrt{\frac{53}{10}} \\ \\ x1=-2+\sqrt{\frac{53}{10}}\\ \\ x2=-2-\sqrt{\frac{53}{10}}\)
therefore
the answer is
the value of A is \(10\)