Question

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SecundariaBaldor 5+3 ptos


Resolver las siguientes ecuaciones mediante formula general
1) 176x=121+64x al cuadrado
2) 8x+5=36x al cuadrado
3) 27x al cuadrado+12x-7=0
4) 15x=25x al cuadrado+2
5) 8x al cuadrado-2x-3=0
6) 105=x+2x al cuadrado
*PORFAVOR PODRÍAN DESARROLLAR CADA UNA*
Resolver las siguientes ecuaciones mediante la fórmula particular.
1) X al cuadrado-3x+2=0
2) X al cuadrado-2x-15=0
3) X al cuadrado-19x=88
4) X al cuadrado+4x= 285
5) 5x(x-1) -2(2x al cuadrado-7x) =-8
6) X al cuadrado-(7x+6) =X+59
7) (x-1) al cuadrado+11x+199=3xal cuadrado-(x-2) al cuadrado.
8) (x-2) (X+2) -7(x-1) =21
9) 2xal cuadrado-(x-2) (X+5) =7(X+3)
10) (x-1) (X+2) -(2x-3) (X+4) -4+14=0
*PODRÍAN DESARROLLAR CADA UNA PORFAVOR

Answer 1

1.) 176x=121+64x^2
176x - 64x^2=121
176x -64x^2 -121 = 0
ax^2 + bx + c
a×c = -64 × - 121 = 7744
b=176
-64x^2 + 88x + 88x - 121
(-64x^2 + 88x) + (88x - 121)
8x (-8x + 11) - 11(-8x + 11)
(-8x + 11)(8x - 11) = 0
8x - 11 =0
-8x = 11
x= 11÷ 8
Forma decimal = 1,375
Formula numérica mixta: x=1 (3÷8)
2.) 8x + 5 = 36x^2
8x + 5 - 36x^2= 0
-36x^2 + 8x + 5 = 0
a × c= 36 × (-5)= -180
b= - 8
-(36x^2 +(-18 + 10) x - 5) = 0
- (36x^× -18x + 10x - 5) = 0
- ((36x^2 - 18x) + (10x -5))= 0
- (18x ( 2x -1) +5 ( 2x - 1)) = 0
- (2x-1)(18x + 5) = 0
2x - 1 = 0
2x = 1
x = 1 ÷ 2
18x + 5 = 0
18x = -5
x= - 5÷ 18
x=1÷2; -5÷18
x=0,5; -0,27
3.) 27x^2 + 12x - 7= 0
a × c = 27 × (-7) = - 189
b = 12
27x^2 + (-9 + 21)x - 7= 0
27x^2 - 9x + 21x - 7= 0
(27x^2 - 9x) + ( 21x - 7) = 0
9x (3x - 1) + 7(3x - 1) = 0
(3x - 1)( 9x + 7) = 0
3x - 1 = 0
3x = 1
x = 1÷3
9x + 7= 0
9x = -7
x = - 7÷9
x=1÷3; -7÷9
x= 0,3; -0,7
4.) 15x = 25x^2 + 2
-25x^2 + 15x + 2 = 0
a × c = -25 × -2 = 50
b = 15
- 25x^2 + (5 + 10) x - 2=0
-25x^2 + 5x +10x -2=0
(-25x^2 + 5x) + (10x - 2) = 0
5x (-5x + 1) - 2 (-5x + 1) = 0
(-5x + 1) (5x - 2) = 0
-5x + 1 = 0
- 5x = - 1
x= 1 ÷ 5
5x - 2 = 0
5x = 2
x = 2÷5
x = 1÷5; 2÷5
x = 0,2 ; 0,4
5.) 8x^2 - 2x - 3 = 0
a×c = 8 × -3 = -24
b = -2
8x^2 + (- 6 + 4) x - 3 = 0
8x^2 - 6x + 4x - 3= 0
(8x^2 - 6x) + (4x - 3) = 0
2x (4x - 3) + 1( 4x - 3) = 0
(4x - 3) (2x + 1) = 0
4x - 3 = 0
4x = 3
x = 3÷4
2x + 1 = 0
2x = -1
x = -1÷2
x = 3÷4; -1÷2
x = 0,75; - 0,5
6.) 105 = x + 2x^2
-2x^2 - x + 105 = 0
a × c = 2 × - 105= - 210
b= 1
2x^2 + (-14 + 15)x - 105= 0
2x^2 - 14x + 15x - 105= 0
(2x^2 - 14x) + (15x - 105) = 0
2x(x - 7) + 15 (x-7) = 0
(x - 7) (2x + 15) = 0
x - 7 = 0
x = 0 + 7
x = 7
2x + 15 = 0
2x= - 15
x = -15 ÷ 2
x= 7; -15 ÷2
x= 7; - 7 (1÷2)
----------------------------------------------------------------------
1.) x^2-3x+2= 0
x^2 + bx + c = 0
- 2 ; -1= 0
(x - 2) (x - 1) = 0
x - 2 = 0
x= 0 + 2
x = 2
x - 1 = 0
x = 0 + 1
x = 1
x= 2, 1
2.) x^2 - 2x - 15 = 0
x^2 + bx + c = 0
- 5; 3 = 0
(x - 5) (x + 3) = 0
x - 5 = 0
x = 0 + 5
x = 5
x + 3 = 0
x = 0 - 3
x = -3
x= 5; -3
3.) x^2 - 19x = 88
x^2 + bx + c = 0
x^2 - 19x - 88 = 0
- b +- raiz b^2 - 4ac ÷ 2a
a= 1
b = - 19
c = - 88
19 +- raiz (-19)^2 - 4(1)(-88) ÷ 2(1)
19 +- raiz 361 + 352 ÷ 2
x = 22, 8 ; - 3, 85
4.) x^2 + 4x = 285
x^2 + bx + c = 0
-15; 19 = 0
(x - 15) (x + 19) = 0
x - 15 = 0
x = 0 + 15
x= 15
x + 19 = 0
x = 0 - 19
x = -19
x = 15, - 19
5.) 5x(1-x) - 2(2x^2 - 7x) = - 8
5x × 1 + 5x (-x) - 2 ( 2x^2 - 7x) = - 8
5x + 5x (-x) - 2 (2x^2 - 7x) = - 8
5x + 5 (xx) × - 1 -2 (2x - 7x)
a^m a^n = a ^ m+n
5x - 5x ^2 -2 (2x^2 - 7x) = - 8
5x - 5x^2 + (-4x^2 + 14x) = -8
-5x^2 - 4x^2 + 19x = -8
-9x^2 + 19 x= - 8
-9x^2 + 19x + 8 = 0
-b +- raiz b^2 - 4ac ÷ 2a
- (-19) +- raiz (-19)^2 -4 (9) (-8) ÷ 2 (9)
x = 19 +- raiz 649 ÷ 18
x = 2,4 ; -0,35
6.)x^2 - (7x+6) = x + 56
x^2 -7x - 6 = x + 56
x^2 - 7x - 6 - x= 56
x^2 - 8x - 6= 56
x^2 - 8x - 6 - 56 = 0
x^2 - 8x - 62= 0
- b +- raiz b^2 - 4ac ÷ 2a
a=1 ; b= -8; c= -62
- (-8) +- raiz (-8)^2 - 4 (1)(-62) ÷ 2(1)
8 +- raiz 64 + 248 ÷ 2
x = 8 +- raiz 312 ÷ 2
x = 4 +- raiz 78
x = 12, 8; -4,83
7.) (x-1)^2+11x+199= 3x^2 - (x - 2)^2
(x-1)^2 +11x + 199 - 3x^2 + (x-2)^2 = 0
xx + x × -1 -1x - 1 × - 1 + 11x + 199 - 3x^2 + ( x-2)^2=0
x^2 - 2x + 1 + 11x + 199 - 3x^2 + ( x-2)(x-2) = 0
x^2 - 2x + 1 + 11x + 199 - 3x^2 + ( x^2 -4x +4x) = 0
-x^2 + 9x + 1 + 199 - 4x + 4 = 0
-x^2 + 5x + 204 = 0
-17;2 = 0
-( x - 17) (x+12) = 0
x-17=0
x= 0 + 17
x=17
x + 12 = 0
x= 0 - 12
x = -12
x = 17; -12
8.) (x-2)(x+2)-7(x-1)=21
x^2-4-7(x-1)= 21
x^2 - 7x + 3 = 21
x^2 - 7x + 3 - 21 = 0
x^2 - 7x - 18 = 0
-9; 2 = 0
(x-9)(x+2)=0
x-9=0
x=0+9
x=9
x+2=0
x=0 - 2
x = - 2
x= 9, - 2
9.)2x^2 -(x-2)(x+5) = 7(x+3)
2x^2 + ( - x^2 - 3x + 10) = 7(x+3)
2x^2 - x^2 - 3x + 10 = 7 ( x + 3)
x^2 - 3x + 10 = 7 ( x + 3)
x^2 - 3x + 10 = 7x + 21
x^2 - 3x + 10 - 7x = 21
x^2 - 10x + 10= 21
x^2 - 10x + 10 - 21 = 0
x^2 - 10x - 11 = 0
-11; 1 = 0
(x - 11) ( x + 1) = 0
x - 11 = 0
x = 0 + 11
x = 11
x + 1 = 0
x = 0 - 1
x = - 1
x = 11; -1
10.)(x-1)(x+2) - (2x - 3) (x + 4) - 4 + 14 = 0
x^2 + x - 2- (2x - 3) (x + 4) - 4 + 14 = 0
x^2 + x - 2 + (2x + 3) (x + 4) -4 + 14 = 0
x^2 + x - 2 + (-2xx - 2x × 4 + 3x + 3 × 4) - 4 + 14 = 0
x^2 + x - 2 +(-2x^2 - 5x + 12) - 4 + 14= 0
-x^2 - 4x - 2 + 12 - 4 + 14 = 0
- x^2 - 4x + 20 = 0
x^2 + 4x - 20 = 0
- b +- raiz b^2 - 4ac ÷ 2a
a = 1
b = 4
c = -20
- 4 +- raiz (-4) ^2 - 4(1)(-20) ÷ 2(1)
x = - 4 +- raiz 16 + 80 ÷ 2
x = - 4 +- raiz 96 ÷ 2
x = - 4 +- raiz 4^2 × 6
x = - 4 +- 4 raiz 6 ÷ 2
x = - 2 +- 2 raiz 6
x = 2,89 ; - 6, 89