The expression as a perfect square trinomial is
.
The expression as a perfect square trinomial is ![\rm x^2-20x+100\\](https://tex.z-dn.net/?f=%5Crm%20x%5E2-20x%2B100%5C%5C)
The expression as a perfect square trinomial is
.
<h2>
Given that</h2>
The given equations are as follows;
![\rm x^2 + 2x + \\\\ x^2 -20x +\\\\ x^2 + 5x +\\\\](https://tex.z-dn.net/?f=%5Crm%20x%5E2%20%2B%202x%20%2B%20%5C%5C%5C%5C%0Ax%5E2%20-20x%20%2B%5C%5C%5C%5C%0Ax%5E2%20%2B%205x%20%2B%5C%5C%5C%5C)
<h3>
We have to determine</h3>
What values are needed to make each expression a perfect square trinomial?
According to the question
To know more about the values are needed to make a perfect square trinomial following all the steps given below.
A perfect square trinomial is equal to;
![\rm (x+a)^2 = x^2+a^2+2ax](https://tex.z-dn.net/?f=%5Crm%20%28x%2Ba%29%5E2%20%3D%20x%5E2%2Ba%5E2%2B2ax)
1. The given equation is,
![\rm x^2 + 2x +](https://tex.z-dn.net/?f=%5Crm%20x%5E2%20%2B%202x%20%2B)
Then,
Compare with the formula of a perfect square trinomial.
![\rm x^2+2ax+a^2= x^2+4x\\ \\ 4x=2ax\\ \\ a = \dfrac{4x}{2x}\\ \\ a=2](https://tex.z-dn.net/?f=%5Crm%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%2B4x%5C%5C%0A%5C%5C%0A4x%3D2ax%5C%5C%0A%5C%5C%0Aa%20%3D%20%5Cdfrac%7B4x%7D%7B2x%7D%5C%5C%0A%5C%5C%0Aa%3D2)
Substitute the value of a
![\rm x^2+2ax+a^2= x^2+4x+(2)^2\\ \\ x^2+2ax+a^2= x^2+4x+4\\](https://tex.z-dn.net/?f=%5Crm%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%2B4x%2B%282%29%5E2%5C%5C%0A%5C%5C%0A%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%2B4x%2B4%5C%5C)
The expression as a perfect square trinomial is
.
2. The given equation is,
![\rm x^2 - 20x +](https://tex.z-dn.net/?f=%5Crm%20x%5E2%20-%2020x%20%2B)
Then,
Compare with the formula of a perfect square trinomial.
![\rm x^2+2ax+a^2= x^2-20x\\ \\ -20x=2ax\\ \\ a = \dfrac{-20x}{2x}\\ \\ a=-10](https://tex.z-dn.net/?f=%5Crm%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2-20x%5C%5C%0A%5C%5C%0A-20x%3D2ax%5C%5C%0A%5C%5C%0Aa%20%3D%20%5Cdfrac%7B-20x%7D%7B2x%7D%5C%5C%0A%5C%5C%0Aa%3D-10)
Substitute the value of a
![\rm x^2+2ax+a^2= x^2 -20x+(-10)^2\\ \\ x^2+2ax+a^2= x^2-20x+100\\](https://tex.z-dn.net/?f=%5Crm%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%20-20x%2B%28-10%29%5E2%5C%5C%0A%5C%5C%0A%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2-20x%2B100%5C%5C)
The expression as a perfect square trinomial is
.
3. The given equation is,
![\rm x^2 + 5x +](https://tex.z-dn.net/?f=%5Crm%20x%5E2%20%2B%205x%20%2B)
Then,
Compare with the formula of a perfect square trinomial.
![\rm x^2+2ax+a^2= x^2+5x\\ \\ 5x=2ax\\ \\ a = \dfrac{5x}{2x}\\ \\ a=\dfrac{5}{2}](https://tex.z-dn.net/?f=%5Crm%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%2B5x%5C%5C%0A%5C%5C%0A5x%3D2ax%5C%5C%0A%5C%5C%0Aa%20%3D%20%5Cdfrac%7B5x%7D%7B2x%7D%5C%5C%0A%5C%5C%0Aa%3D%5Cdfrac%7B5%7D%7B2%7D)
Substitute the value of a
![\rm x^2+2ax+a^2= x^2+4x+(\dfrac{5}{2})^2\\ \\ x^2+2ax+a^2= x^2+4x+\dfrac{25}{4}\\](https://tex.z-dn.net/?f=%5Crm%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%2B4x%2B%28%5Cdfrac%7B5%7D%7B2%7D%29%5E2%5C%5C%0A%5C%5C%0A%20x%5E2%2B2ax%2Ba%5E2%3D%20x%5E2%2B4x%2B%5Cdfrac%7B25%7D%7B4%7D%5C%5C)
The expression as a perfect square trinomial is
.
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