Question

Isoke is solving the quadratic equation by completing the square.10x2 + 40x – 13 = 0 10x2 + 40x = 13 A(x2 + 4x) = 13What is the value of A?

Answer 1

Completing the square is done as follows:

1. Write the equation in a way that the constants are in the right side while the terms with x are on the left. 

10x2 + 40x = 13

2. Make sure that the coefficient of the x^2 term is 1.
10(x^2 + 4x) = 13

3. 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.

Answer 2

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 $10$