Question

(x−3)^2+2=8 quadratic

Answer 1

x = 3 ± √6.

or 0.55, 5.45 to the nearest hundredth.

Explanation:

(x−3)^2+2=8

(x - 3)^2 = 8 - 2 = 6

(x - 3)^2 = 6

Taking square roots of both sides:

x - 3 = +/- √6

x = 3 ± √6.

Answer 2

ㅤ

Given quadratic equation:-

⇢
`\rm{(x - 3) 2 + 2 = 8}`

ㅤ

Simplifying the given equation:-

ㅤ

1) Simplify both sides of the equation.

⇢
`\rm{x^(2) - 6x + 11 = 8}`

ㅤ

2) Subtract (8) from both sides, we get:

⇢
`\rm{x^(2) - 6x + 11 - 8 = 8 - 8}`

⇢
`\rm{x^(2) - 6x + 3 = 0}`

ㅤ

3) In the equation: (a = 1), (b = -6), (c = 3):

⇢
`\rm{1x^(2) + - 6x + 3 = 0}`

ㅤ

4) Use quadratic formula:

⇢
`\rm{x = \frac{-b \pm \sqrt{b^(2) - 4ac}}{2a}}`

⇢
`\rm{x = \frac{-(-6) \pm\sqrt{(-6)^(2) - 4 (1) (3)}}{2 * 1}}`

⇢
`\rm{x = (6 \pm √(4))/(2)}`

⇢
`{\boxed{\rm{x = 3 \pm √(6)}}}`