Question

Rewrite! Write an new and equivalent equation that is easier to solve

Answer 1

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x = -7, -1

Explanation:

`\sf {(x + 2)}^(2) + 4(x + 2) - 5 = 0`

let (x + 2) = y

So equation will be

`\sf {y}^(2) + 4y - 5 = 0`

Further it becomes quadratic equation

we will solve it by breaking middle term method

`\sf \implies {y}^(2) + 5y - y - 5 = 0 \\ \\ \sf \implies y(y + 5) - 1(y + 5) = 0 \\ \\ \sf \implies (y + 5)(y - 1) = 0`

Now put the value of y

`\sf \implies (x + 2 + 5)(x + 2 - 1) = 0 \\ \\ \sf \implies (x + 7)(x + 1) = 0`

(x + 7) =0⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(x + 1) = 0

x = -7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = -1

Answer 2

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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 -

`\bold{(x + 2) {}^(2) + 4(x + 2) - 5 = 0} \\`

solve the parenthesis so as to obtain simpler terms

`\bold{\implies \: ( x {}^(2) + 4x + 4 ) + 4x + 8 - 5 = 0}\\`

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

`\bold{\implies \: x {}^(2) + 8x - 7 = 0}`

hope helpful ~