Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2x+5x^2-4=6+7x
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Equation log2(x^2+3x)=2
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Equation ctg(x)=-sqrt3/3
- Equation 4+(2x-(4x-1))+x=-5-x
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- Graphing y =:
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Identical expressions
- two x+5x^2- four = six +7x
- 2x plus 5x squared minus 4 equally 6 plus 7x
- two x plus 5x squared minus four equally six plus 7x
- 2x+5x2-4=6+7x
- 2x+5x²-4=6+7x
- 2x+5x to the power of 2-4=6+7x
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Similar expressions
- 2x-5x^2-4=6+7x
- 1/(x-6)+(7x+35)/(x^2-36)=0
- x+2*x^2+3*x^3+4*x^4+5*x^5+6*x^6+7*x^7+8*x^8+9*x^9+10*x^10+11*x^11+12*x^12+13*x^13=105,9141
- 5*x^12-12*x^10-5*x^8-8*x^6+7*x^4-12*x^2-1=0
- 2x+5x^2+4=6+7x
- 2x+5x^2-4=6-7x
2x+5x^2-4=6+7x 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
$$\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6$$
to
$$\left(- 7 x - 6\right) + \left(\left(5 x^{2} + 2 x\right) - 4\right) = 0$$
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
$$a = 5$$
$$b = -5$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -1$$
left part with negative sign.
The equation is transformed from
$$\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6$$
to
$$\left(- 7 x - 6\right) + \left(\left(5 x^{2} + 2 x\right) - 4\right) = 0$$
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
$$a = 5$$
$$b = -5$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (5) * (-10) = 225
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -1$$
Vieta's Theorem
rewrite the equation
$$\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - x - 2 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -2$$
$$\left(5 x^{2} + 2 x\right) - 4 = 7 x + 6$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - x - 2 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -2$$
The graph