Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 5*sin(x)+cos(x)=5
-
Equation 4*x^2+7=7+24*x
-
Equation 2x^2-3x-2=0
-
Equation x^2-7*x+10=0
- Express {x} in terms of y where:
- 17*x-19*y=-12
- 3*x+19*y=4
- 13*x-1*y=-20
- -16*x-9*y=-1
- Factor polynomial:
- x^2+6
- Derivative of:
-
x^2+6
-
5x
- Integral of d{x}:
-
5x
- Graphing y =:
- 5x
-
Identical expressions
- x^ two + six =5x
- x squared plus 6 equally 5x
- x to the power of two plus six equally 5x
- x2+6=5x
- x²+6=5x
- x to the power of 2+6=5x
-
Similar expressions
- x^2-6=5x
- (-5*x-3)*(2*x-5)=0
- -2*x+16=5*x-19
x^2+6=5x 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
$$x^{2} + 6 = 5 x$$
to
$$- 5 x + \left(x^{2} + 6\right) = 0$$
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
$$a = 1$$
$$b = -5$$
$$c = 6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
$$x_{2} = 2$$
left part with negative sign.
The equation is transformed from
$$x^{2} + 6 = 5 x$$
to
$$- 5 x + \left(x^{2} + 6\right) = 0$$
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
$$a = 1$$
$$b = -5$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (6) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
$$x_{2} = 2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 6$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = 6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = 6$$
The graph