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Katie solved the equation by completing the square.

x^2+12x−7=0



Which equation shows one of the steps Katie could have taken to complete the square?




x^2+12x+144=7

x^2+12x+144=7+144

x^2+12x+36=7+36

x^2+12x+36=7

Respuesta :

frika

Katie has equation [tex]x^2+12x-7=0[/tex] and wants to solve it completing the perfect square. In order to do it, first rewrite 7 in right side:

[tex]x^2+12x=7.[/tex]

Then note that [tex]12x=2\cdot 6\cdot x,[/tex] so Katie has to add [tex]6^2=36[/tex] to both sides (because [tex]x^2+12x+36=x^2+2\cdot 6\cdot x+6^2=(x+6)^2[/tex]):

 [tex]x^2+12x+36=7+36,\\ \\(x+6)^2=43.[/tex]

Answer: correct choice is C.

abidemiokin

Option C is correct. One of the steps Katie could have taken to complete the square is x²+12x +36 = 7 + 36

Given the equation that Katie solved using the completing the square method expressed as:

x²+12x−7=0

The steps to be taken are as follows

Step 1: Add 7 to both sides

x²+12x−7 + 7=0 + 7

x²+12x = 7

Step 2: Complete the square by adding the square of the half of the coefficient of x to both sides

Coefficient of x = 12

half of coefficient of x = 12/2 = 6

square of the half of coefficient of x = 6^2

Add 6^2 to both sides

x²+12x +6^2 = 7 + 6^2

(x+6)^2 = 7 + 36

x²+12x +36 = 7 + 36

Hence one of the steps Katie could have taken to complete the square is x²+12x +36 = 7 + 36

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