Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=5
-
Equation k^2+k=0
-
Equation 5x=0
-
Equation x^2-15=2x
- Express {x} in terms of y where:
- -4*x+3*y=9
- -2*x-19*y=-11
- -5*x+15*y=-15
- -1*x+7*y=-11
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
-
Identical expressions
- x^ two = five
- x squared equally 5
- x to the power of two equally five
- x2=5
- x²=5
- x to the power of 2=5
-
Similar expressions
- x^2-9*x+14=0
x^2=5 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
$$x^{2} = 5$$
to
$$x^{2} - 5 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{5}$$
$$x_{2} = - \sqrt{5}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 5$$
to
$$x^{2} - 5 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-5) = 20
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{5}$$
$$x_{2} = - \sqrt{5}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -5$$
Rapid solution
[src]
___ x1 = -\/ 5
$$x_{1} = - \sqrt{5}$$
___ x2 = \/ 5
$$x_{2} = \sqrt{5}$$
x2 = sqrt(5)
Sum and product of roots
[src]
sum
___ ___ - \/ 5 + \/ 5
$$- \sqrt{5} + \sqrt{5}$$
=
0
$$0$$
product
___ ___ -\/ 5 *\/ 5
$$- \sqrt{5} \sqrt{5}$$
=
-5
$$-5$$
-5
The graph