Réponse :

Explications étape par étape

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Résoudre :

-3x + 5 = 2

-3x + 5 + 3x = 2 + 3x

5 - 2 = 2 + 3x - 2

3 = 3x

3/3 = 3x/3

x = 1

6x + 3 = -7x + 4

6x + 3 + 7x = -7x + 4 + 7x

13x + 3 - 3 = 4 - 3

13x = 1

13x/13 = 1/13

x = 1/13

(2x - 5)(6x + 3) = 0

Produit de facteur est nul si au moins l’un de ces facteurs est nul

2x - 5 = 0 ou 6x + 3 = 0

2x - 5 + 5 = 0 + 5 ou 6x + 3 - 3 = 0 - 3

2x = 5 ou 6x = -3

2x/2 = 5/2 ou 6x/6 = -3/6

x = 5/2 ou x = -1/2

2x(-4x + 12) - 7(-4x + 12) = 0

-8x^2 + 24x + 28x - 84 = 0

-8x^2 + 52x - 84 = 0

8x^2 - 52x + 84 = 0

4(x^2 - 13x + 21) = 0

x^2 - 13x + 21 = 0

x^2 - 2 * x * 13/2 + (13/2)^2 - (13/2)^2 + 21 = 0

(x - 13/2)^2 - 169/4 + 84/4 = 0

(x - 13/2)^2 - 85/4 = 0

(x - 13/2 - (V85)/2)(x - 13/2 + (V85)/2) = 0

x1 = 13/2 + (V85)/2

x2 = 13/2 - (V85)/2

(Avec V : racine)

(3x + 6)(8x + 4) + (5x + 9)(3x + 6) = 0

(3x + 6)(8x + 4 + 5x + 9) = 0

(3x + 6)(13x + 13) = 0

3(x + 2) * 13(x + 1) = 0

39(x + 2)(x + 1) = 0

x + 2 = 0 ou x + 1 = 0

x = -2 ou x = -1

(2x - 4)(x + 10) = (2x - 4)^2

(2x - 4)(x + 10) - (2x - 4)^2 = 0

(2x - 4)(x + 10 - 2x + 4) = 0

(2x - 4)(-x + 14) = 0

2(x - 2)(-x + 14) = 0

x - 2 = 0 ou -x + 14 = 0

x = 2 ou x = 14

(x - 11)^2 = 9

(x - 11)^2 - 9 = 0

(x - 11)^2 - 3^2 = 0

(x - 11 - 3)(x - 11 + 3) = 0

(x - 14)(x - 8) = 0

x - 14 = 0 ou x - 8 = 0

x = 14 ou x = 8