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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? 4x ^2 +47x...Question
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
4x ^2 +47x+104=7x
4x ^2 +47x+104=7x
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GPT 3.5
First, let's simplify the equation to make it easier to work with:
4x^2 + 47x + 104 - 7x = 0
This can be simplified to:
4x^2 + 40x + 104 = 0
The intermediate step in completing the square for this equation is to divide the entire equation by the coefficient of x^2, which is 4 in this case:
x^2 + 10x + 26 = 0
Now we can complete the square by adding the square of half of the coefficient of x, which is 5 in this case. Add (5^2) = 25 to both sides of the equation:
x^2 + 10x + 25 + 26 = 25
x^2 + 10x + 25 = -26
Next, we can rewrite the left side of the equation as a perfect square:
(x + 5)^2 = -26
This is the intermediate step after completing the square for the given equation.
4x^2 + 47x + 104 - 7x = 0
This can be simplified to:
4x^2 + 40x + 104 = 0
The intermediate step in completing the square for this equation is to divide the entire equation by the coefficient of x^2, which is 4 in this case:
x^2 + 10x + 26 = 0
Now we can complete the square by adding the square of half of the coefficient of x, which is 5 in this case. Add (5^2) = 25 to both sides of the equation:
x^2 + 10x + 25 + 26 = 25
x^2 + 10x + 25 = -26
Next, we can rewrite the left side of the equation as a perfect square:
(x + 5)^2 = -26
This is the intermediate step after completing the square for the given equation.
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