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Similar expressions
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9x-25+3x^2=17+2x^2+8x equation
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The solution
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[src]
2 2 9*x - 25 + 3*x = 17 + 2*x + 8*x
$$3 x^{2} + 9 x - 25 = 2 x^{2} + 8 x + 17$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$3 x^{2} + 9 x - 25 = 2 x^{2} + 8 x + 17$$
to
$$\left(- 2 x^{2} - 8 x - 17\right) + \left(3 x^{2} + 9 x - 25\right) = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = 1$$
$$c = -42$$
, then
$$D = b^2 - 4\ a\ c = $$
$$1^{2} - 1 \cdot 4 \left(-42\right) = 169$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 6$$
Simplify
$$x_{2} = -7$$
Simplify
left part with negative sign.
The equation is transformed from
$$3 x^{2} + 9 x - 25 = 2 x^{2} + 8 x + 17$$
to
$$\left(- 2 x^{2} - 8 x - 17\right) + \left(3 x^{2} + 9 x - 25\right) = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = 1$$
$$c = -42$$
, then
$$D = b^2 - 4\ a\ c = $$
$$1^{2} - 1 \cdot 4 \left(-42\right) = 169$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 6$$
Simplify
$$x_{2} = -7$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -42$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -42$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = -42$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = -42$$
Sum and product of roots
[src]
sum
-7 + 6
$$\left(-7\right) + \left(6\right)$$
=
-1
$$-1$$
product
-7 * 6
$$\left(-7\right) * \left(6\right)$$
=
-42
$$-42$$
The graph