Question

(x² + 6x + 1) = (x – 3)

Answer 1

`\sf{\underline{\boxed{\green{\large{\bold{ Solution}}}}}}`

`\sf\implies x^2 + 6x + 1 = x - 3`

`\sf\implies x^2 + 6x - x + 1 + 3 = 0`

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`\sf\implies x^2 + 5x + 4 = 0`

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compare the eq with
`\sf{\underline{\bold{ax^2 + bx + c = 0 }}}`

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☯ a = 1

☯ b = 5

☯ c = 4

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now :-

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`\sf{\underline{\boxed{\pink{\large{\mathfrak{x = ( - b \pm \sqrt D )/(2a )}}}}}}`

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`\sf{\underline{\boxed{\pink{\large{\mathfrak{ D = b^2 - 4ac }}}}}}`

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finding value of D.

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`\sf\implies D = b^2 - 4ac`

`\sf\implies D = (5)^2 - 4 * 1 * 4`

`\sf\implies D = 25 - 16`

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`\sf\implies D = 9`

`\sf{\underline{\boxed{\blue{\large{\bold{ D = 9}}}}}}`

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putting values in the eq.

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`\sf\implies x = ( -b \pm\sqrt D )/(2a)`

`\sf\implies x = \frac{ -( 5) \pm\sqrt {9} }{2* 1 }`

`\sf\implies x = ( -5 \pm 3 )/(2)`

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✒
`\sf x = ( -5 + 3 )/( 2 )`

`\implies x = \frac {-2}{2}`

`\implies x = -1`

`\sf{\underline{\boxed{\purple{\large{\bold{ x = -1 }}}}}}`

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✒
`\sf x = ( -5 - 3 )/( 2 )`

`\implies x = \frac {-8}{2}`

`\implies x = -4`

`\sf{\underline{\boxed{\purple{\large{\bold{ x = -4 }}}}}}`

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`\sf{\underline{\boxed{\purple{\large{\bold{ x = -1 \: or \:-4 }}}}}}`

Answer 2

Hello!

`\large\boxed{x = -4, -1}`

x² + 6x + 1 = x - 3

Bring all terms to one side by subtracting x and adding 3:

x² + 6x - x + 1 + 3 = x - x - 3 + 3

x² + 5x + 4 = 0

Factor:

(x + 4)(x + 1) = 0

Set each factor to 0:

x + 4 = 0

x = -4

x + 1 = 0

x = -1