Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 7x+3=30-2x
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Equation x^4-5x^2+4=0
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Equation (x^2-9)^2+(x^2-2*x-15)^2=0
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Equation 5x-25+2x^2=17+13x
- Express {x} in terms of y where:
- 4*x+13*y=13
- 17*x-19*y=1
- 10*x+9*y=-4
- -12*x+3*y=-9
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Identical expressions
- 5x- twenty-five + two x^2= seventeen +13x
- 5x minus 25 plus 2x squared equally 17 plus 13x
- 5x minus twenty minus five plus two x squared equally seventeen plus 13x
- 5x-25+2x2=17+13x
- 5x-25+2x²=17+13x
- 5x-25+2x to the power of 2=17+13x
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Similar expressions
- 5x-25-2x^2=17+13x
- 5x-25+2x^2=17-13x
- 5x+25+2x^2=17+13x
5x-25+2x^2=17+13x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$2 x^{2} + \left(5 x - 25\right) = 13 x + 17$$
to
$$\left(- 13 x - 17\right) + \left(2 x^{2} + \left(5 x - 25\right)\right) = 0$$
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
$$a = 2$$
$$b = -8$$
$$c = -42$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -3$$
left part with negative sign.
The equation is transformed from
$$2 x^{2} + \left(5 x - 25\right) = 13 x + 17$$
to
$$\left(- 13 x - 17\right) + \left(2 x^{2} + \left(5 x - 25\right)\right) = 0$$
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 - it is the discriminant.
Because
$$a = 2$$
$$b = -8$$
$$c = -42$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (2) * (-42) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -3$$
Vieta's Theorem
rewrite the equation
$$2 x^{2} + \left(5 x - 25\right) = 13 x + 17$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x - 21 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -21$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -21$$
$$2 x^{2} + \left(5 x - 25\right) = 13 x + 17$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x - 21 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -21$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -21$$
Sum and product of roots
[src]
sum
-3 + 7
$$-3 + 7$$
=
4
$$4$$
product
-3*7
$$- 21$$
=
-21
$$-21$$
-21
The graph