Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-21=4x
-
Equation x^2-13*x=0
-
Equation 6^x=1
- Equation x^3+6*x^2-x-6=0
- Express {x} in terms of y where:
- 19*x-7*y=2
- -3*x+3*y=10
- 3*x-15*y=-9
- 6*x-13*y=-19
- Integral of d{x}:
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4x
- Sum of series:
- 4x
- Derivative of:
-
4x
-
Identical expressions
- x^ two - twenty-one =4x
- x squared minus 21 equally 4x
- x to the power of two minus twenty minus one equally 4x
- x2-21=4x
- x²-21=4x
- x to the power of 2-21=4x
-
Similar expressions
- x^2+21=4x
- 4*x^2+12*x-7=0
- log(4*x)=2
x^2-21=4x 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
$$x^{2} - 21 = 4 x$$
to
$$- 4 x + \left(x^{2} - 21\right) = 0$$
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
$$a = 1$$
$$b = -4$$
$$c = -21$$
, 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
$$x^{2} - 21 = 4 x$$
to
$$- 4 x + \left(x^{2} - 21\right) = 0$$
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
$$a = 1$$
$$b = -4$$
$$c = -21$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (-21) = 100
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
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -21$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -21$$
$$p x + q + x^{2} = 0$$
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