Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -x/7+x=15/7
-
Equation -33-y=-19
-
Equation x^2=2x+8
-
Equation 6=8-5(7x-1)
- Express {x} in terms of y where:
- -2*x+18*y=13
- -2*x-15*y=-1
- 5*x+4*y=-12
- 10*x-2*y=11
- Graphing y =:
- x^2
- 2x+8
- Derivative of:
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x^2
- Integral of d{x}:
-
x^2
-
Identical expressions
- x^ two =2x+ eight
- x squared equally 2x plus 8
- x to the power of two equally 2x plus eight
- x2=2x+8
- x²=2x+8
- x to the power of 2=2x+8
-
Similar expressions
- 2x^2+x-21=0
- 5cos^2*x+8*cos(x)=4
- -x^2+8x+6=0
- a^2*(1-x)*(1-a*x+a*x^2)=1
- 2^x=2*x+8
- (2*x+8)^2=0
- x^2=2x-8
- (x^2+9*x+18)/(x+5)=(x+8)/x
- 12x=-36+3x^2
x^2=2x+8 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
$$x^{2} = 2 x + 8$$
to
$$x^{2} + \left(- 2 x - 8\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -2$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 2 x + 8$$
to
$$x^{2} + \left(- 2 x - 8\right) = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-8) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -8$$
The graph