Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+x=12
-
Equation (-2x+1)*(-2x-7)=0
- Equation x-y+1=0
-
Equation 9x+4=48-2x
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- -5*x-2*y=9
- Derivative of:
-
-x
- Integral of d{x}:
-
-x
- Graphing y =:
- -x
-
Identical expressions
- sqrt(10x+ eleven)=-x
- square root of (10x plus 11) equally minus x
- square root of (10x plus eleven) equally minus x
- √(10x+11)=-x
- sqrt10x+11=-x
-
Similar expressions
- sqrt(10x+11)=+x
- sqrt(10x-11)=-x
sqrt(10x+11)=-x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{10 x + 11} = - x$$
$$\sqrt{10 x + 11} = - x$$
We raise the equation sides to 2-th degree
$$10 x + 11 = x^{2}$$
$$10 x + 11 = x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 10 x + 11 = 0$$
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
$$a = -1$$
$$b = 10$$
$$c = 11$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = 11$$
Because
$$\sqrt{10 x + 11} = - x$$
and
$$\sqrt{10 x + 11} \geq 0$$
then
$$- x \geq 0$$
or
$$x \leq 0$$
$$-\infty < x$$
The final answer:
$$x_{1} = -1$$
$$\sqrt{10 x + 11} = - x$$
$$\sqrt{10 x + 11} = - x$$
We raise the equation sides to 2-th degree
$$10 x + 11 = x^{2}$$
$$10 x + 11 = x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 10 x + 11 = 0$$
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
$$a = -1$$
$$b = 10$$
$$c = 11$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (-1) * (11) = 144
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = 11$$
Because
$$\sqrt{10 x + 11} = - x$$
and
$$\sqrt{10 x + 11} \geq 0$$
then
$$- x \geq 0$$
or
$$x \leq 0$$
$$-\infty < x$$
The final answer:
$$x_{1} = -1$$