ANSWER
[tex]x =5 \pm \sqrt{35} [/tex]
EXPLANATION
The given quadratic equation is:
[tex] {x}^{2} - 10x + 25 = 35[/tex]
Group the constants on the RHS,
[tex] {x}^{2} - 10x= 35 - 25[/tex]
[tex] {x}^{2} - 10x= 10[/tex]
Add the square of half the coefficient of x to both sides of the equation,
[tex]{x}^{2} - 10x + ( - {5)}^{2} = 10 + ( - {5)}^{2} [/tex]
[tex]{x}^{2} - 10x + 25= 10 + 25[/tex]
We factor the perfect square to get:
[tex]{(x - 5)}^{2} =35[/tex]
[tex]x - 5 = \pm \sqrt{35} [/tex]
[tex]x =5 \pm \sqrt{35} [/tex]
