Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x+y=3
-
Equation x^2-5x+4=0
-
Equation 9-4x=3x-40
-
Equation x^2=8
- Express {x} in terms of y where:
- -17*x+18*y=10
- 18*x+12*y=18
- -11*x-3*y=14
- -20*x-13*y=15
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
-
Identical expressions
- x^ two = eight
- x squared equally 8
- x to the power of two equally eight
- x2=8
- x²=8
- x to the power of 2=8
-
Similar expressions
- x^4-2*x^2+1=0
- 3x^2+18x=0
- (x^3+4)/x^2=0
- x^2+8xsin(xy)+16=0
- x^2+21=10x
x^2=8 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
$$x^{2} = 8$$
to
$$x^{2} - 8 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 8$$
to
$$x^{2} - 8 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-8) = 32
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -8$$
Rapid solution
[src]
___ x1 = -2*\/ 2
$$x_{1} = - 2 \sqrt{2}$$
___ x2 = 2*\/ 2
$$x_{2} = 2 \sqrt{2}$$
x2 = 2*sqrt(2)
Sum and product of roots
[src]
sum
___ ___ - 2*\/ 2 + 2*\/ 2
$$- 2 \sqrt{2} + 2 \sqrt{2}$$
=
0
$$0$$
product
___ ___ -2*\/ 2 *2*\/ 2
$$- 2 \sqrt{2} \cdot 2 \sqrt{2}$$
=
-8
$$-8$$
-8
The graph