Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tan(x)=4
-
Equation -24-y=-16
-
Equation x^2+4x+4=0
-
Equation 4(x-6)=x-9
- Express {x} in terms of y where:
- 10*x-15*y=16
- 9*x+17*y=13
- -10*x+15*y=10
- -13*x-6*y=13
- Integral of d{x}:
-
10x
- Derivative of:
-
10x
- Canonical form:
- 10x
-
Identical expressions
- x^ two + twenty-one =10x
- x squared plus 21 equally 10x
- x to the power of two plus twenty minus one equally 10x
- x2+21=10x
- x²+21=10x
- x to the power of 2+21=10x
-
Similar expressions
- 8sqrt(x^4-10*x^3+13)-8sqrt((x^2+3)^2-12)=0
- x^2-10*x/6-5-2*x/3+x+1=0
- x^2-21=10x
x^2+21=10x 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
$$x^{2} + 21 = 10 x$$
to
$$- 10 x + \left(x^{2} + 21\right) = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -10$$
$$c = 21$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 21 + \left(-10\right)^{2} = 16$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 7$$
Simplify
$$x_{2} = 3$$
Simplify
left part with negative sign.
The equation is transformed from
$$x^{2} + 21 = 10 x$$
to
$$- 10 x + \left(x^{2} + 21\right) = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -10$$
$$c = 21$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 1 \cdot 4 \cdot 21 + \left(-10\right)^{2} = 16$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 7$$
Simplify
$$x_{2} = 3$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -10$$
$$q = \frac{c}{a}$$
$$q = 21$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 10$$
$$x_{1} x_{2} = 21$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -10$$
$$q = \frac{c}{a}$$
$$q = 21$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 10$$
$$x_{1} x_{2} = 21$$
Sum and product of roots
[src]
sum
3 + 7
$$\left(3\right) + \left(7\right)$$
=
10
$$10$$
product
3 * 7
$$\left(3\right) * \left(7\right)$$
=
21
$$21$$
The graph