8x^2 + 22x - 21 = 0Solve the quadratic equation by factoring.?

(4x-3)(2x+7)=0


x=3/4, -7/2

8x^2 + 22x - 21 = 0 Solve the quadratic equation by factoring.
(2x + 7)(4x - 3)

x = -(7/2), 3/4

appropriate, it may be -one hundred twenty five because you moved it over from the appropriate hand of the equation over to the left-hand area. Now you're able to have: 2x^2 - 3 - one hundred twenty five=0 upload -3 and -one hundred twenty five (combining like words) to get -128 so now you need to have: 2x^2 - 128 you may element out an undemanding area of two to get: 2(x^2-sixty 4) you may then element 2(x^2 - sixty 4) to get 2(x-8)(x+8) Your very final answer must be: 2(x-8)(x+8)

(4x - 3)(2x + 7) = 0
x = 3/4 , x = - 7/2

8x^2 + 22x - 21 = 0
(2x + 7)(4x - 3) = 0

2x + 7 = 0
2x = -7
x = -7/2 (-3.5)

4x - 3 = 0
4x = 3
x = 3/4 (0.75)

∴ x = -7/2 (-3.5) , 3/4 (0.75)

people sometimes doesn't how how to factor when there is coefficient for x^2 but this can be solve by factoring the cofficient of x^2 and find the roots , notice that finding the roots of 8x^2 + 22x - 21 = 0 is the same as finding the roots of x^2 + 22x/8 - 21/8

x={-22 + sqrt(22^2 -4*8*-21)}/(2*8) or x = {-22 - sqrt(22^2 -4*8*-21)}/(2*8)

x=3/4 or x= -7/2

8x^2 + 22x - 21 = 4*2*(x-3/4)(x+7/2) = (4x-3)(2x+7)

so you can pretend that you factor by splitting 8x^2 to 4x and 2 x ;

and -21 to -3 and -7 and you will find that the iner products add to 22x

By factoring,
8x^2 + 22x - 21 = 0
x^2 + 22/8x - 21/8 = 0/8
x^2 + 22/8x - 21/8 = 0
x^2 + 22/8x + (22/8/2)^2 - 289/64 = 0
x^2 + 22/8x + (121/64) - 289/64 = 0
x^2 + 22/8x + (11/8)^2 - (17/8)^2 = 0
[x^2 + 22/8x + (11/8)^2] - [(17/8)^2] = 0
(x + 11/8)^2 - (17/8)^2 = 0
Therefore, [(x + 11/8) + (17/8)] * [ (x+11/8) -(17/8)] = 0
(x + 28/8) * (x - 6/8) = 0
(x + 7/2) * (x - 3/4) = 0
x + 7/2 = 0 or x - 3/4 = 0
x = -7/2 or x =3/4.

OR,

By completing the square (another way of factoring),
8x^2 + 22x - 21 = 0
x^2 + 22/8x - 21/8 = 0/8
x^2 + 22/8x = 21/8
x^2 + 22/8x +(22/8/2)^2 = 21/8 + (22/8/2)^2
x^2 + 22/8x + (22/8*1/2)^2 = 21/8 + (22/8* 1/2)^2
x^2 + 22/8x + (11/8)^2 = 21/8 + (11/8)^2
(x + 11/8)^2 = 21/8 + 121/64
(x + 11/8)^ 2 = 168/64 + 121/64
(x + 11/8)^2 = 289/64
(x+11/8) = square root of 289/64
x+11/8 = (+-)17/8
x = (17/8 - 11/8) or (-17/8-11/8)
x = 6/8 or x = -28/8
x = 3/4 or x = - 7/2
x = -7/2 or x = 3/4

(2x + 7)(4x - 3)

x= -7/2, 3/4

(4x - 3)(2x + 7 )

4x+3=0 2x-7=0
4x= -3 2x=7
x = -3/4 x = 7/2

2x(4x+11)-21=0