Answer:[tex]x= \sqrt{88}/3-3[/tex] will be the last step.
Explanation :
Given quadratic equation 9x^2+54x=7
⇒ [tex]9(x^2+6x)=7[/tex]( By the associative property)
⇒[tex]9(x^2+6x)+81=7+81[/tex] ( by adding 81 on both sides)
⇒[tex]9(x^2+6x+9) = 88[/tex] (taking 9 as common in left side of equation.)
⇒[tex]9(x+3)^2=88[/tex]
⇒[tex](x+3)^2=88/9⇒ x+3=\sqrt{88/9}[/tex] ⇒[tex]x=\sqrt{88/9}-3\impliesx= \sqrt{88}/3-3[/tex]
The quadratic equation with the complete squares is:
9*(x + 3)^2 = 88
Remember that:
(a + b)^2 = a^2 + 2ab + b^2
Here we start with:
9x^2 + 54x = 7
The first step is:
9*(x^2 + 6x) = 7 (just take out a common factor)
Now let's do a "half-step"
9*(x^2 + 2*3x) = 7
Now we must add 3^2 and subtract 3^2 (so we don't change the equation).
9*(x^2 + 2*3*x + 3^2 - 3^2) = 7
9*(x^2 + 2*3*x + 3^2) - 9*9 = 7
9*(x + 3)^2 - 81 = 7
9*(x + 3)^2 = 88
This is the equation with the completed squares.
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1214333
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