Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 13/(x+6)=2
-
Equation -x=17
-
Equation x^2=18
- Equation (134545-x)+23=98
- Express {x} in terms of y where:
- 14*x+5*y=11
- 8*x-7*y=-1
- 20*x-5*y=-7
- -1*x+1*y=18
- Graphing y =:
- x^2
- Derivative of:
-
x^2
-
18
- Integral of d{x}:
-
x^2
- Sum of series:
-
18
- The double integral of:
- 18
-
Identical expressions
- x^ two = eighteen
- x squared equally 18
- x to the power of two equally eighteen
- x2=18
- x²=18
- x to the power of 2=18
-
Similar expressions
- lg(4x+3)=lg(x^2)
- x^2-9*x+14=0
x^2=18 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
$$x^{2} = 18$$
to
$$x^{2} - 18 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3 \sqrt{2}$$
$$x_{2} = - 3 \sqrt{2}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 18$$
to
$$x^{2} - 18 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -18$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-18) = 72
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3 \sqrt{2}$$
$$x_{2} = - 3 \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -18$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -18$$
Sum and product of roots
[src]
sum
___ ___ - 3*\/ 2 + 3*\/ 2
$$- 3 \sqrt{2} + 3 \sqrt{2}$$
=
0
$$0$$
product
___ ___ -3*\/ 2 *3*\/ 2
$$- 3 \sqrt{2} \cdot 3 \sqrt{2}$$
=
-18
$$-18$$
-18
Rapid solution
[src]
___ x1 = -3*\/ 2
$$x_{1} = - 3 \sqrt{2}$$
___ x2 = 3*\/ 2
$$x_{2} = 3 \sqrt{2}$$
x2 = 3*sqrt(2)
The graph