solving equations?

Question

solve the equation x^2 +7x - 12 =0
give your answer correct to 4 significant figures.


does the quadratic formula have to be used?

Answer 1

Here are the two roots in exact answer form, and rounded significant figure form.

x = (-7 + root(97)) / 2 or 1.424
x = (-7 - root(97)) / 2 or -8.424

This one can't be factored just by looking at it. The quadratic formula needs to be used. Completing the square is the same thing as the quadratic formula, but stretched out so that you can see how it works.

Answer 2

completing the square

x² + 7x - 12 = 0

x² + 7x - 12 + 12 = 0 + 12

x² + 7x = 12

x² + 7x +______ = 12 + _____

x² + 7x + 49/4 = 12 + 49/4

(x + 7/2)(x + 7/2) = 12 + 49/4

(x + 7/2)² = 48/4 + 49/4

(x + 7/2)² = 97/4

(√x + 7/2)² = ± √97 / √4

x + 7/2 = ± √97 / 2

x + 7/2 - 7/2 = - 7/2 ± √97 / 2

x = - 7/2 ± 9.84885802 / 2

- - - - - - - - -

Solving for +

x = - 7/2 + 9.848857802 / 2

x = 2.848857802 / 2

x = 1.424428901

- - - - - - - - - -

Solving for -

x = - 7/2 - 9.848857802 /2

x = - 16.8488578 / 2

x = - 8.424428901

- - - - - - - - - - - -s-

Answer 3

No, the quadratic formula does not have to be used. You could complete the square:

x^2 + 7x = 12
x^2 + 7x + 3.5^2 = 12 + 3.5^2
(x + 3.5)^2 = 24.25
x + 3.5 = +/- sqrt(24.25)
x = +/- sqrt(24.25) - 3.5
x = 1.4244, -8.4244

Answer 4

you may complete the squares.
(x + 7/2)^2 - 49/4 -12 = 0
=> (x + 7/2)^2 = 97/4
=> x + 7/2 = +sqrt(97)/2 or x + 7/2 = -sqrt(97)/2
=> x = -3.5 + sqrt(97)/2 or -3.5 - sqrt(97)/2

Answer 5

Yes because it doesn't factorise.

Unless you want to complete the square that is.

I'd use the formula.

Answer 6

yeah it does, when they say correct to 4 sf it usually means its not a nice whole number or fraction... all the best! xD

Answer 7

i ges so since it cannot be solved by factoring!