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Similar expressions
- (x-2)(2x-8)-14=0
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(x+2)(2x-8)-14=0 equation
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The solution
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[src]
(x + 2)*(2*x - 8) - 14 = 0
$$\left(x + 2\right) \left(2 x - 8\right) - 14 = 0$$
Detail solution
Expand the expression in the equation
$$\left(x + 2\right) \left(2 x - 8\right) - 14 = 0$$
We get the quadratic equation
$$2 x^{2} - 4 x - 30 = 0$$
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
$$a = 2$$
$$b = -4$$
$$c = -30$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -3$$
$$\left(x + 2\right) \left(2 x - 8\right) - 14 = 0$$
We get the quadratic equation
$$2 x^{2} - 4 x - 30 = 0$$
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
$$a = 2$$
$$b = -4$$
$$c = -30$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (2) * (-30) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -3$$
Sum and product of roots
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sum
-3 + 5
$$-3 + 5$$
=
2
$$2$$
product
-3*5
$$- 15$$
=
-15
$$-15$$
-15
The graph