Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3*x/3=(1-x)/2
-
Equation tan(x)=-5
-
Equation x^2=-81
-
Equation sqrt(x-2)=x-4
- Express {x} in terms of y where:
- -13*x+15*y=1
- 11*x-6*y=-1
- -8*x-15*y=-12
- 18*x-15*y=-7
- Derivative of:
-
sqrt(x-2)
-
x-4
- Graphing y =:
- sqrt(x-2)
- x-4
- Integral of d{x}:
-
sqrt(x-2)
-
x-4
-
Identical expressions
- sqrt(x- two)=x- four
- square root of (x minus 2) equally x minus 4
- square root of (x minus two) equally x minus four
- √(x-2)=x-4
- sqrtx-2=x-4
-
Similar expressions
- sqrtx-2/3=0
- sqrt(x-2)=x+4
- sqrt(x+2)=x-4
sqrt(x-2)=x-4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{x - 2} = x - 4$$
$$\sqrt{x - 2} = x - 4$$
We raise the equation sides to 2-th degree
$$x - 2 = \left(x - 4\right)^{2}$$
$$x - 2 = x^{2} - 8 x + 16$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 9 x - 18 = 0$$
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
$$a = -1$$
$$b = 9$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
Simplify
$$x_{2} = 6$$
Simplify
Because
$$\sqrt{x - 2} = x - 4$$
and
$$\sqrt{x - 2} \geq 0$$
then
$$x - 4 \geq 0$$
or
$$4 \leq x$$
$$x < \infty$$
The final answer:
$$x_{2} = 6$$
$$\sqrt{x - 2} = x - 4$$
$$\sqrt{x - 2} = x - 4$$
We raise the equation sides to 2-th degree
$$x - 2 = \left(x - 4\right)^{2}$$
$$x - 2 = x^{2} - 8 x + 16$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 9 x - 18 = 0$$
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
$$a = -1$$
$$b = 9$$
$$c = -18$$
, then
D = b^2 - 4 * a * c =
(9)^2 - 4 * (-1) * (-18) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
Simplify
$$x_{2} = 6$$
Simplify
Because
$$\sqrt{x - 2} = x - 4$$
and
$$\sqrt{x - 2} \geq 0$$
then
$$x - 4 \geq 0$$
or
$$4 \leq x$$
$$x < \infty$$
The final answer:
$$x_{2} = 6$$
The graph