What number should be added to the expression \(x^2 + 14x\) to change it into a perfect square trinomial?

x^2+14x
To make it as perfect square binomial first divide the numerical coefficient of 14 by 2 which is 7. Then square the result[7] which is 49 and add it to the equation x^2+14x+49 After that think of a number that has a square root of 49 then when u multiply the second term in the perfect square by the first and 2 it results to 14. So the answer is [x+7]^2

Answered by HunterX | 2024-06-10

In order to transform the expression x² + 14x into a perfect square trinomial, we must add a number that completes the square.
A perfect square trinomial is of the form (x + a)², which expands to x² + 2ax + a².
To find the value of a², we take the coefficient of the x term, divide it by 2, and then square the result.
In this case, we have 14x as the middle term, so we divide 14 by 2 to get 7, and then square 7 to get 49.
Therefore, the number that should be added to x² + 14x to make it a perfect square trinomial is 49.

Answered by ToddBoyce | 2024-06-24

To make the expression x 2 + 14 x a perfect square trinomial, add 49. The expression then becomes x 2 + 14 x + 49 , which factors to ( x + 7 ) 2 .
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Answered by HunterX | 2024-12-23