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

Question

asked Oct 24, 2023 43.9k views

2 Answers

Kruczy · Answer 1 · 2023-10-27T06:15:17+0000

${\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}$

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

Anton Okolnychyi · Answer 2 · 2023-10-30T21:10:47+0000

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

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 ~