Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x+7*4=40
-
Equation -x^3+4*x^2+4*x-16=0
-
Equation x/7=6
-
Equation 12x-5x=3,192
- Express {x} in terms of y where:
- -12*x-19*y=16
- 18*x+19*y=-1
- -19*x+12*y=16
- 20*x+2*y=13
- Sum of series:
- (x-2)^2
- Integral of d{x}:
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(x-2)^2
- Derivative of:
-
(x-2)^2
-
Identical expressions
- (x- two)^ two = three
- (x minus 2) squared equally 3
- (x minus two) to the power of two equally three
- (x-2)2=3
- x-22=3
- (x-2)²=3
- (x-2) to the power of 2=3
- x-2^2=3
-
Similar expressions
- (x+2)^2=3
(x-2)^2=3 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
$$\left(x - 2\right)^{2} = 3$$
to
$$\left(x - 2\right)^{2} - 3 = 0$$
Expand the expression in the equation
$$\left(x - 2\right)^{2} - 3 = 0$$
We get the quadratic equation
$$x^{2} - 4 x + 1 = 0$$
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
$$a = 1$$
$$b = -4$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{3} + 2$$
$$x_{2} = 2 - \sqrt{3}$$
left part with negative sign.
The equation is transformed from
$$\left(x - 2\right)^{2} = 3$$
to
$$\left(x - 2\right)^{2} - 3 = 0$$
Expand the expression in the equation
$$\left(x - 2\right)^{2} - 3 = 0$$
We get the quadratic equation
$$x^{2} - 4 x + 1 = 0$$
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
$$a = 1$$
$$b = -4$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (1) = 12
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{3} + 2$$
$$x_{2} = 2 - \sqrt{3}$$
Rapid solution
[src]
___ x1 = 2 - \/ 3
$$x_{1} = 2 - \sqrt{3}$$
___ x2 = 2 + \/ 3
$$x_{2} = \sqrt{3} + 2$$
x2 = sqrt(3) + 2
Sum and product of roots
[src]
sum
___ ___ 2 - \/ 3 + 2 + \/ 3
$$\left(2 - \sqrt{3}\right) + \left(\sqrt{3} + 2\right)$$
=
4
$$4$$
product
/ ___\ / ___\ \2 - \/ 3 /*\2 + \/ 3 /
$$\left(2 - \sqrt{3}\right) \left(\sqrt{3} + 2\right)$$
=
1
$$1$$
1
The graph