Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -15x=45
-
Equation x^2=15
-
Equation x^4=16
-
Equation 3/5*x=1
- Express {x} in terms of y where:
- 18*x+17*y=-14
- -1*x-6*y=18
- 16*x-17*y=-15
- -4*x-4*y=19
-
Identical expressions
- two x^ two - eighteen =2
- 2x squared minus 18 equally 2
- two x to the power of two minus eighteen equally 2
- 2x2-18=2
- 2x²-18=2
- 2x to the power of 2-18=2
-
Similar expressions
- 2x^2+18=2
2x^2-18=2 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
$$2 x^{2} - 18 = 2$$
to
$$\left(2 x^{2} - 18\right) - 2 = 0$$
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
$$a = 2$$
$$b = 0$$
$$c = -20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{10}$$
Simplify
$$x_{2} = - \sqrt{10}$$
Simplify
left part with negative sign.
The equation is transformed from
$$2 x^{2} - 18 = 2$$
to
$$\left(2 x^{2} - 18\right) - 2 = 0$$
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
$$a = 2$$
$$b = 0$$
$$c = -20$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (2) * (-20) = 160
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{10}$$
Simplify
$$x_{2} = - \sqrt{10}$$
Simplify
Vieta's Theorem
rewrite the equation
$$2 x^{2} - 18 = 2$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 10 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -10$$
$$2 x^{2} - 18 = 2$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 10 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -10$$
Sum and product of roots
[src]
sum
____ ____ 0 - \/ 10 + \/ 10
$$\left(- \sqrt{10} + 0\right) + \sqrt{10}$$
=
0
$$0$$
product
____ ____ 1*-\/ 10 *\/ 10
$$\sqrt{10} \cdot 1 \left(- \sqrt{10}\right)$$
=
-10
$$-10$$
-10
The graph