quadratic formula?

Question

can anyone show me how to solve: x^2 + x - 42 = 0

step by step using the quadratic formula

I keep trying but its really not working!!
Thanks!

Answer 1

x^2 + x - 42 = 0

This equation factors easily into

(x + 7)(x - 6) = 0

Whence

x = -7, x = 6

So there is no need to use the quadratic formula

However, the quadratic formula for solving the general second order equation

ax^2 + bx + c = 0

is

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

In your problem

x = [-1 +- sqrt(1 + 168)]/2 = [-1 +- sqrt(169)]/2 = [-1 +- 13]/2

Whence

x = -7, x = 6

Answer 2

You don't need quadratic formula: just factor. What two numbers multiply to be -42 but add to be 1? 7 and -6. So the equation can be rewritten as (x-6)(x+7)=0 and your zeros are 6 and -7, respectively.

If you're dead set on quadratic, the equation is x= -b+ or - (b^2-4ac)^(1/2) all over 2a. Sound confusing enough? Good. the equation isn't too bad, as here a=1, b=1, and c=-42. I've seen uglier. So start plugging: x= -1 +or- (1+4*42)^(1/2) all over 2. This in turn simplifies to -1+or- (169)^(1/2) all over 2, which is -1+or- 13, again over 2. So you get -14/2 which equals -7 and 12/2, which equals 6.

Now which method seems easier to you?

Answer 3

The quadratic formula says that the solution to
ax^2 + bx + c = 0
is
x = ( - b +/- sqrt(b^2 - 4ac) ) / 2a .....(1)

For your equation
a = 1, b = 1, c = -42.

Substituting these values in (1):
x = ( - 1 +/- sqrt(1^2 - 4*1*(-42)) ) / 2*1
= ( - 1 +/- sqrt(1 + 4*42) ) / 2
= ( - 1 +/- sqrt(1 + 168) ) / 2
= ( - 1 +/- sqrt(169) ) / 2
= ( - 1 +/- 13 ) / 2
= ( -1 + 13 ) / 2 or (- 1 - 13) / 2
= 12 / 2 or -14/2
= 6 or -7.

Answer 4

The equation is of form ax^2+bx+c=0
a=1 b=1 c=-42 (match the coefficients)
The solution is
[-b+sqrt(b^2-4ac)] / 2a
and
[-b-sqrt(b^2-4ac)] /2a
First solution
[-1+sqrt(1-4(1)(-42)] /2
=[-1+sqrt(169)]/2 =[-1+13]/2 =12/2 = 6 *
Second solution
=[-1-sqrt(169)]/2 =[-1-13]/2 =-14/2 = -7 *

check: x^2+x-42 =0
if x=6, 6^2+6-42 =36+6-42=0
if x=-7, -7^2-7-42 =49-7-42=0

Answer 5

It is worth noting that this equation factorises:-
(x + 7) (x - 6) = 0
x = - 7 , x = 6
Now check with quadratic formula:-
x = [- 1 ± √(1 + 168) ] / 2
x = [- 1 ± √169] / 2
x = [- 1 ± 13 ] / 2
x = 12 / 2 , x = - 14 / 2
x = 6 , x = - 7 (as before)

Answer 6

The formula is (-b±√(b^2-4ac))/2a, with a being the coefficient of x^2, b the coefficient of x, and c the number.
So what you'd do is set a=1, b=1, c=-42, and solve:
x=(-1±√(1^2-4*1*(-42)))/(2*1)
x=(-1±√(1+168))/2
x=(-1±13)/2
x1=6, x2=-7

Answer 7

ok the quadratic formula is: -

x = [ -b (+/-) sqrt (b^2 - 4*a*c) ] / 2*a

look at the coeffecients of your equation (the number in front) and compare it to the structure ax^2 + bx + c...

you should see a = 1 (1x^2 is the same as x^2)
you should see b = 1 (1x is the same as x)
you should see c = -42

plug all these numbers into the equation you get ...

x =[ -1 (+/-) sqrt( (1)^2 - 4 * 1 * (-42)) ] / 2*1

simplyfying etc you eventually end up with ...

x = [-1 (+/-) sqrt(167) ] / 2

this is effectively the same as these two equations

x = [-1 + sqrt(167) ] / 2
x = [-1 - sqrt(167) ] / 2

solving these two should give you the numerical answers of

x = 5.961 and x = - 6.961

Answer 8

the quadratic formula is used to solve the possible variable solutions in quadratic equations, which are equations in which the a variable is squared. the formula itself is: x = -b (+/-) (square root of (b^2-4ac) / 2a so given 2x^2 +9x + 4 a= 2 b= 9 c= 4 so then plugging it into the equation: x= (-9) (+/-) square root (9^2-4(2) (4) / 2(2) simplified: x= -9 (+/-) square root (49) / 4 x= (-9 + 7)/ 4 or (-9 - 7) /4 solved: x = -1/2, or -4 hope that helps! good luck...

Answer 9

[-b +- Sqrt(b^2 - 4ac)]/2a

a = 1
b = 1
c = -42

[-1 +- Sqrt( 1 - 4(-42)(1)]/2

seperate it
(-1/2) +- Sqrt(1 + 168) / 2

Sqrt (169) = 13

(-1/2) +- 13/2

-1/2 + 13/2 = 12/2 = 6

-1/2 - 13/2 = -14/2 = -7


answers 6 and -7

(x - 6)*(x+7) = x^2+x - 42 = 0

Answer 10

so, the formula is
D=(B^2)-4(A.C) then to find X you must take the square root of D

1 - 4(-42)
D=1+168=169 then

(-1+-13)/2 = 6 and -7 there you go!