Question

What is the first step in solving the quadratic equation x2 – 40 = 0?

Answer 1

Answer:

Given the quadratic equation: $x^2-40=0$

Addition property of equality states that you add the same number to both sides of an equation.

Step 1.

$x^2-40=0$

Add 40 to both sides of an equation:

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

Simplify:

$x^2=40$                ......[1]

Step 2.

Take square root both sides in equation [1]; we have

$\sqrt{x^2} =\sqrt{40}$

Simplify:

$x=\pm \sqrt{40} =\pm 2\sqrt{5}$

Hence, the roots for the given equation is x = $+2\sqrt{5}$ , $-2\sqrt{5}$ .

Therefore, for solving the quadratic equation the first step is; Adding 40 to both sides of an equation.

Answer 2

$x^2- 40 = 0\ \ \ \Leftrightarrow\ \ \ x^2-(2 \sqrt{10} )^2=0\\\\\ \ \ \Leftrightarrow\ \ \ (x-2 \sqrt{10} )(x+2 \sqrt{10} =0\\\\ \ \ \Leftrightarrow\ \ \ x=2 \sqrt{10} \ \ \ \ \ or\ \ \ \ \ x=-2 \sqrt{10$