Question

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Answer 1

1)

⇒ x² - 6x = -8

`\sf add \ 9 \ on \ both \ sides`

⇒ x² - 6x + 9 = -8 + 9

`\sf simplify \ and \ complete \ square`

⇒ x² - 3x - 3x + 9 = 1

`\sf factor \ common \ term`

⇒ x(x - 3) - 3(x - 3) = 1

`\sf collect \ into \ groups`

⇒ (x - 3)² = 1

`\sf square \ root \ both \ sides`

⇒ x - 3 = ±√1

`\sf simplify`

⇒ x - 3 = ±1

`\sf change \ side`

⇒ x = 1 + 3, -1 + 3

`\sf simplify`

⇒ x = 4, 2

2)

`\rightarrow \sf 4x^2 + 12x + 11 = 0`

`\rightarrow \sf 4\left(x^2+3x+(11)/(4)\right) = 0`

`\rightarrow \sf 4\left(x^2+3x+(11)/(4)+\left((3)/(2)\right)^2-\left((3)/(2)\right)^2\right) = 0`

`\rightarrow \sf 4\left(x+(3)/(2)\right)^2+2 = 0`

`\rightarrow \sf \left(x+(3)/(2)\right)^2 = -(2)/(4)`

`\rightarrow \sf \left(x+(3)/(2)\right)^2 = -(1)/(2)`

`\rightarrow \sf x+(3)/(2) = \pm \sqrt{-(1)/(2) }`

`\rightarrow \sf x+(3)/(2) = \pm i\sqrt{(1)/(2) }`

`\rightarrow \sf x= \pm i\sqrt{(1)/(2) }-(3)/(2)`