Respuesta :

MidnightShowers

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  • Given - an equation in it's general form

  • To do - convert the given equation into a form that is easy to solve

Given equation -

[tex]\bold{(x + 2) {}^{2} + 4(x + 2) - 5 = 0} \\ [/tex]

solve the parenthesis so as to obtain simpler terms

[tex]\bold{\implies \: ( x {}^{2} + 4x + 4 ) + 4x + 8 - 5 = 0}\\ [/tex]

solve the like terms and you'll obtain the required equation !

[tex]\bold{\implies \: x {}^{2} + 8x - 7 = 0}[/tex]

hope helpful ~

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x = -7, -1

Step-by-step explanation:

[tex] \sf {(x + 2)}^{2} + 4(x + 2) - 5 = 0[/tex]

let (x + 2) = y

So equation will be

[tex] \sf {y}^{2} + 4y - 5 = 0[/tex]

Further it becomes quadratic equation

we will solve it by breaking middle term method

[tex] \sf \implies {y}^{2} + 5y - y - 5 = 0 \\ \\ \sf \implies y(y + 5) - 1(y + 5) = 0 \\ \\ \sf \implies (y + 5)(y - 1) = 0[/tex]

Now put the value of y

[tex] \sf \implies (x + 2 + 5)(x + 2 - 1) = 0 \\ \\ \sf \implies (x + 7)(x + 1) = 0[/tex]

(x + 7) =0⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(x + 1) = 0

x = -7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = -1

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