Question

Helen is solving a quadratic equation. She wants to find the value of x by taking the square root of both sides of the equation. Which equation allows her to do this?
1) x^2+ 24x + 144 = 17

2) x^2 + 7x + 12 = 34

3) x^2+ 7x + 49 = 10

4) x^2+ 25x + 10 = 20

Answer 1

Answer:

1) $x^2+ 24x + 144 = 17$

Step-by-step explanation:

The answer is 1) because the left side in the equation

$x^2+ 24x + 144 = 17$

can be represented a perfect square:

$x^2+ 24x + 144=(x+12)^2$

so we have that the original equation becomes:

$(x+12)^2=17$

and then, taking the square root of both sides of the equation:

$\sqrt{(x+12)^2} =$ ± $\sqrt{17}$

$x+12=$ ±$\sqrt{17}$

we are left with an equation where we can find the values of x.

so we clear for x and we get:

$x=$ ±$\sqrt{17}$ $-12$

thus,  the two values of x are:

$x_{1}=\sqrt{17}-12 \\x_{2}=-\sqrt{17}-12$