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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

Respuesta :

Answer:

1) [tex]x^2+ 24x + 144 = 17[/tex]

Step-by-step explanation:

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

[tex]x^2+ 24x + 144 = 17[/tex]

can be represented a perfect square:

[tex]x^2+ 24x + 144=(x+12)^2[/tex]

so we have that the original equation becomes:

[tex](x+12)^2=17[/tex]

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

[tex]\sqrt{(x+12)^2} =[/tex] ± [tex]\sqrt{17}[/tex]

[tex]x+12=[/tex] ±[tex]\sqrt{17}[/tex]

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

so we clear for x and we get:

[tex]x=[/tex] ±[tex]\sqrt{17}[/tex] [tex]-12[/tex]

thus,  the two values of x are:

[tex]x_{1}=\sqrt{17}-12 \\x_{2}=-\sqrt{17}-12[/tex]

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