Question

X2-8x+10=0 solve for x

Answer 1

`\sf x=√(6) +4`

`\sf x=4-√(6)`

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 √(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 √(\left(-8\right)^2-4* \:1\cdot \:10)}{2* \:1}`

Square -8, and multiply -4 by 10:

`\sf x=\cfrac{(-8)\pm√(64-40) }{2}`

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

`\sf x=\cfrac{-(-8)\pm2√(6) }{2}`

-(-8)= 8

`\sf x=\cfrac{8\pm2√(6) }{2}`

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

`\sf x=√(6) +4`

`\sf x=4-√(6)`

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