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How to use it?
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Equation x^2+x=6
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Identical expressions
- (x− six)(x+ twelve)= zero
- (x−6)(x plus 12) equally 0
- (x− six)(x plus twelve) equally zero
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Similar expressions
- (x−6)(x-12)=0
(x−6)(x+12)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 6\right) \left(x + 12\right) = 0$$
We get the quadratic equation
$$x^{2} + 6 x - 72 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 6$$
$$c = -72$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = -12$$
$$\left(x - 6\right) \left(x + 12\right) = 0$$
We get the quadratic equation
$$x^{2} + 6 x - 72 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 6$$
$$c = -72$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (-72) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = -12$$
Sum and product of roots
[src]
sum
-12 + 6
$$-12 + 6$$
=
-6
$$-6$$
product
-12*6
$$- 72$$
=
-72
$$-72$$
-72