Use the quadratic formula to solve the following quadratic equation: 8x2 + 2x - 3 = 0.?

the formula is -b+/-sqrt(b^2-4ac)
-------------------------
2a

here a=8, b=2, c=-3

So we have -2+/-sqrt(2^2-4*(-3*8))
-----------------------------
16

or -2+/- sqrt(100)
---------------------
16

sqrt(100)=10

so this comes to -12/16 and 8/16

or -3/4 and 1/2

Find factors:
8x² + 2x - 3 = 0
8x² + 2x = 3
x² + 1/4x = 3/8
x² + 1/8x = 3/8 + (1/8)²
x² + 1/8x = 24/64 + 1/64
(x + 1/8)² = 25/64
x + 1/8 = 5/8

Factors:
= x + 1/8 - 5/8
= x - 1/2
= 2x - 1

= x + 1/8 + 5/8
= x + 3/4
= 4x + 3

Values of x:
2x - 1 = 0, 2x = 1, x = 1/2
4x + 3 = 0, 4x = - 3, x = - 3/4

Answer: x = 1/2, - 3/4; (2x - 1)(4x + 3) are the factors.

Proof (x = 1/2):
8(1/2²) + 2(1/2) = 3
8(1/4) + 1 = 3
2 + 1 = 3

Proof (x = - 3/4):
8(- 3/4)² + 2(- 3/4) = 3
8(9/16) - 3/2 = 3
9/2 - 3/2 = 3
6/2 = 3

Proof (F.O.I.L. the factors):
= (2x - 1)(4x + 3)
= 8x² + 6x - 4x - 3
= 8x² + 2x - 3

For the equation ax² + bx + c = 0, the solution is given by:

x = [ -b ± √(b² - 4ac) ] / [2a]

In your question a = 8, b = 2 and c = -3, substituting these values in to the formula:

x = [ -2 ± √(2² - 4(8)(-3)) ] / [2(8)]
x = [ -2 ± √(4 +96) ] / [16]
x = ( -2 ± √100 ) / 16
x = ( -2 ± 10 ) / 16

So the two answers are:

x = ( -2 + 10 ) / 16 = 8/16 = ½
x = ( -2 - 10 ) /16 = -12/16 = -3/4

x = [ -2 +/- sqrt(4 + 96) ] / 16
= [ -2 +/- 10 ] / 16

x = 8/16 = 1/2, or
x = -12/16 = -3/4

8x^2 + 2x - 3 = 0

a = 8
b = 2
c = -3

x = (-b +/- sqrt(b^2 - 4ac))/2a

x = (-2 +/- sqrt(2^2 - 4(8)(-3)))/2(8)

x = (-2 +/- sqrt(4 + 96))/16

x = (-2 +/- sqrt(100))/16

x = (-2 +/- 10)/16

x = 8/16 or -12/16

x = 1/2 or -3/4

x = [ - 2 ± √ (4 + 96 ) ] / 16
x = [ - 2 ± √ (100) ] / 16
x = [ - 2 ± 10 ] / 16
x = 8 / 16 , x = - 12 / 16
x = 1 / 2 , x = - 3 / 4

8x² + 2x - 3 = 0
x = -2/(2•8) ± √[ 2² - 4(8)(-3)] / (2•8)
x = -1/8 ± √(4 + 96) / 16
x = -1/8 ± 10/16
x = 9/16 or x = -11/16

it extremely is interior the variety ax² + bx + c = 0, so a = 8, b = 2, c = -3 The quadratic equation is x = (-b ± ?(b² - 4ac))/(2a) so which you have x = (-2 ± ?(2² - 4*8*(-3)))/(2*8) = (-2 ± ?(4 + ninety six))/sixteen = (-2 ± ?one hundred)/sixteen = (-2 ± 10)/sixteen If it extremely is +, you have 8/sixteen = a million/2 If it extremely is -, you have -12/sixteen = -3/4 the respond is -3/4 or a million/2, so it extremely is C tell Turiski to apply the quadratic formulation stunning, "like it says"

8x^2 + 2x - 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 8
b = 2
c = -3

x = [-2 ±√(4 + 96)]/16
x = [-2 ±√100]/16
x = [-2 ±10]/16

x = [-2 + 10]/16
x = 8/16
x = 1/2 (0.5)

x = [-2 - 10]/16
x = -12/16
x = -3/4 (-0.75)

∴ x = -3/4 (-0.75) , 1/2 (0.5)

i can do this by factoring but ok

8x2+2x-3=0

-2+- /__4+96

-2+- /__100

-2+10 /2 -2-10 /2

8/2=4 -12/2= -6

your answers are 4 and -6