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Equation 5(x+1)(x-3)=4x^2-8x
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Identical expressions
- five (x+ one)(x- three)=4x^ two -8x
- 5(x plus 1)(x minus 3) equally 4x squared minus 8x
- five (x plus one)(x minus three) equally 4x to the power of two minus 8x
- 5(x+1)(x-3)=4x2-8x
- 5x+1x-3=4x2-8x
- 5(x+1)(x-3)=4x²-8x
- 5(x+1)(x-3)=4x to the power of 2-8x
- 5x+1x-3=4x^2-8x
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Similar expressions
- 5*(x+1)*(x-3)=4*x^2-8*x
- 5(x+1)(x+3)=4x^2-8x
- 5(x-1)(x-3)=4x^2-8x
- 5(x+1)(x-3)=4x^2+8x
5(x+1)(x-3)=4x^2-8x equation
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The solution
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2 5*(x + 1)*(x - 3) = 4*x - 8*x
$$\left(x - 3\right) 5 \left(x + 1\right) = 4 x^{2} - 8 x$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x - 3\right) 5 \left(x + 1\right) = 4 x^{2} - 8 x$$
to
$$\left(x - 3\right) 5 \left(x + 1\right) + \left(- 4 x^{2} + 8 x\right) = 0$$
Expand the expression in the equation
$$\left(x - 3\right) 5 \left(x + 1\right) + \left(- 4 x^{2} + 8 x\right) = 0$$
We get the quadratic equation
$$x^{2} - 2 x - 15 = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -3$$
left part with negative sign.
The equation is transformed from
$$\left(x - 3\right) 5 \left(x + 1\right) = 4 x^{2} - 8 x$$
to
$$\left(x - 3\right) 5 \left(x + 1\right) + \left(- 4 x^{2} + 8 x\right) = 0$$
Expand the expression in the equation
$$\left(x - 3\right) 5 \left(x + 1\right) + \left(- 4 x^{2} + 8 x\right) = 0$$
We get the quadratic equation
$$x^{2} - 2 x - 15 = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -15$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-15) = 64
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