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How to use it?
- Equation:
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Equation 3/(x-5)+8/x=2
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Equation 0,144:(3,4-x)=2,4
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Equation (-2x+1)*(-2x-7)=0
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Equation 1/x^2-1/x-6=0
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Identical expressions
- (-2x+ one)*(-2x- seven)= zero
- ( minus 2x plus 1) multiply by ( minus 2x minus 7) equally 0
- ( minus 2x plus one) multiply by ( minus 2x minus seven) equally zero
- (-2x+1)(-2x-7)=0
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Similar expressions
- (-2x-1)*(-2x-7)=0
- (-2x+1)(-2x-7)=0
- (-2x+1)*(2x-7)=0
- (-2x+1)*(-2x+7)=0
- (2x+1)*(-2x-7)=0
- (-2*x+1)*(-2*x-7)=0
(-2x+1)*(-2x-7)=0 equation
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The solution
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[src]
(-2*x + 1)*(-2*x - 7) = 0
$$\left(1 - 2 x\right) \left(- 2 x - 7\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(1 - 2 x\right) \left(- 2 x - 7\right) = 0$$
We get the quadratic equation
$$4 x^{2} + 12 x - 7 = 0$$
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
$$a = 4$$
$$b = 12$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = - \frac{7}{2}$$
$$\left(1 - 2 x\right) \left(- 2 x - 7\right) = 0$$
We get the quadratic equation
$$4 x^{2} + 12 x - 7 = 0$$
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
$$a = 4$$
$$b = 12$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (4) * (-7) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = - \frac{7}{2}$$
Sum and product of roots
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sum
-7/2 + 1/2
$$- \frac{7}{2} + \frac{1}{2}$$
=
-3
$$-3$$
product
-7 --- 2*2
$$- \frac{7}{4}$$
=
-7/4
$$- \frac{7}{4}$$
-7/4
The graph