Step-by-step explanation:
Step 1: Write our Givens
![{x}^{2} + 10x - 7 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2010x%20-%207%20%3D%200)
Move the constant term ,(the term with no variable) to the right side.
Here we have a negative 7, so we add 7 to both sides
![{x}^{2} + 10x = 7](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2010x%20%3D%207)
Next, we take the linear coeffeicent and divide it by 2 then square it.
![( \frac{10}{2} ) {}^{2} = 25](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B10%7D%7B2%7D%20%29%20%7B%7D%5E%7B2%7D%20%20%3D%2025)
Then we add that to both sides
![{x}^{2} + 10x + 25 = 7 + 25](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2010x%20%2B%2025%20%3D%207%20%2B%2025)
![{ {x}^{2} } + 10x + 25 = 32](https://tex.z-dn.net/?f=%20%7B%20%7Bx%7D%5E%7B2%7D%20%7D%20%2B%2010x%20%2B%2025%20%3D%2032)
Next, we factor the left,
![(x + 5)(x + 5) = 32](https://tex.z-dn.net/?f=%28x%20%2B%205%29%28x%20%2B%205%29%20%3D%2032)
we got 5 because 5 add to 10 and multiply to 25 as well.
so we get
![(x + 5) {}^{2} = 32](https://tex.z-dn.net/?f=%28x%20%2B%205%29%20%7B%7D%5E%7B2%7D%20%20%3D%2032)
This is called a perfect square trinomial.
Next, we take the square root of both sides
![x + 5 = ± \sqrt{32}](https://tex.z-dn.net/?f=x%20%2B%205%20%3D%20%C2%B1%20%5Csqrt%7B32%7D%20)
± menas that we have a positive and negative solution.
Subtract 5 form both side so we get
![x = - 5± \sqrt{32}](https://tex.z-dn.net/?f=x%20%3D%20%20-%205%C2%B1%20%5Csqrt%7B32%7D%20)
The greater solution is when sqr root of 32 is positive so the answer to that is
![\sqrt{32} - 5 = 0.7](https://tex.z-dn.net/?f=%20%5Csqrt%7B32%7D%20%20-%205%20%3D%200.7)