Mister Exam
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How to use it?
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Equation 2-3(7+2x)=11
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Identical expressions
- (3x- twelve)*(x+ fourteen)= zero
- (3x minus 12) multiply by (x plus 14) equally 0
- (3x minus twelve) multiply by (x plus fourteen) equally zero
- (3x-12)(x+14)=0
- 3x-12x+14=0
- (3x-12)*(x+14)=O
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Similar expressions
- (3x-12)*(x-14)=0
- (3x+12)*(x+14)=0
(3x-12)*(x+14)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x + 14\right) \left(3 x - 12\right) = 0$$
We get the quadratic equation
$$3 x^{2} + 30 x - 168 = 0$$
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
$$a = 3$$
$$b = 30$$
$$c = -168$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -14$$
$$\left(x + 14\right) \left(3 x - 12\right) = 0$$
We get the quadratic equation
$$3 x^{2} + 30 x - 168 = 0$$
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
$$a = 3$$
$$b = 30$$
$$c = -168$$
, then
D = b^2 - 4 * a * c =
(30)^2 - 4 * (3) * (-168) = 2916
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -14$$
Sum and product of roots
[src]
sum
-14 + 4
$$-14 + 4$$
=
-10
$$-10$$
product
-14*4
$$- 56$$
=
-56
$$-56$$
-56