Question

X2-8x+10=0 solve for x

Answer 1

Answer:

$\sf x=\sqrt{6} +4$

$\sf x=4-\sqrt{6}$

Step-by-step explanation:

$\sf x^2-8x+10=0$

Equations of the form ax^2+bx+c=0 can be solved by the quadratic formula:

$\boxed{\sf \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$

Quadratic formula gives you two solutions one when (±) addition and one when (±) is a subtraction:

$\sf x^2-8x+10=0$

Substitute:

$a:1$

$b:-8$

$c:10$

$\sf x=\cfrac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\times \:1\cdot \:10}}{2\times \:1}$

Square -8, and multiply -4 by 10:

$\sf x=\cfrac{(-8)\pm\sqrt{64-40} }{2}$

Add 64 and - 40, and take the square root of 24:

$\sf x=\cfrac{-(-8)\pm2\sqrt{6} }{2}$

-(-8)= 8

$\sf x=\cfrac{8\pm2\sqrt{6} }{2}$

Now solve when (±) is a plus and then solve when it is a minus:-

$\sf x=\sqrt{6} +4$

$\sf x=4-\sqrt{6}$

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