Question

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

Answer 1

The value of A in solving the considered quadratic equation by completing the squares method is given by: Option

What is completing the squares method for solving the quadratic method?

Suppose the considered quadratic equation is of the form $ax^2 + bx + c = 0$

Then, completing the squares method tries to make a squared term in terms of x in the left side, so that x comes in linear form, instead of quadratic, as shown below:

$ax^2 + bx + c = 0\\ax^2 + bx = -c\\\\\text{Multiplying 4a on both the sides}\\4a^2x^2 + 4abx = -4ac\\\\\text{Adding }b^2\text{ on both the sides}\\4a^2x^2 + 4abx + b^2 = b^2 -4ac\\or\\(2ax +b)^2 = b^2 - 4ac\\2ax + b = \pm \sqrt{b^2 - 4ac}\\\\x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

This provides two solution to the considered quadratic equation. These solutions can be real, or imaginary.

For the considered case, the quadratic equation is:

$10x^2 + 40x - 13 = 0$

Applying the method as Isoke did, we get:

$10x^2 + 40x - 13 = 0\\10x^2 + 40x = 13\\10(x^2 + 4x) = 13$

Therefore, we get the value of A as 10.

Learn more about completing the squares here:

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