Science & Mathematics » Mathematics » What should be added to equation to make it a perfect square 9x^4 + 2x^2 + 25? ....Please!?

# What should be added to equation to make it a perfect square 9x^4 + 2x^2 + 25? ....Please!?

• Find (3x^2 + 5)^2 minus what you are given.
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• 9x^4 = (3x^2)^2
25 = 5^2

(3x^2 + 5)^2 = 9x^4 + 30x^2 + 25

To make the expression a perfect square, you must add 28x^2.
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• That is not an equation. You mean to add a constant to it? Is that the idea?

9x⁴ + 2x² + 25
= (9x⁴ + 2x² + 1/9) + 25 - 1/9
= (3x² + 1/3)² + 25 - 1/9
= (3x² + 1/3)² + 224/9

So, if you were to add -224/9 to the expression you would have (3x² + 1/3)², a perfect square. Is that what you wanted?
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• If you add -224/9, then you get 9x^4 + 2x^2 + (1/9) which is equal to (3x^2 + (1/3))^2
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• There are several things you could add to make it a perfect square. Since you were given a few options, just try each one.
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• 28x^2
or
-32x^2
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• y-25+36/18^2 = 9[x^4+(2/9)x^2+4/18^2]
y-25+1/9 = 9[x^4+(2/9)x^2+1/81]
y - 224/9 = 9(x^2+1/9)^2
y = 9(x^2+1/9)^2 + 224/9
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• 28x^2. Square roots of 9x^4 and 25 are 3x^2 and 5 respectively. A perfect square trinomial can be achieved in one of two ways:

(x - y)^2 = x^2 - 2xy + y^2

(x + y)^2 = x^2 + 2xy + y^2

The only thing that differs is the sign of the middle term. All you do is multiply 3x^2 and 5, then double that product to get 30x^2. You got 2x^2 already, you must add 28x^2 to get the perfect square.
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• 9x^4+2x^2+25+4x^2+(-24)=
9x^4+6x^2+1=
(3x^2+1)^2
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