Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^3=x^2+2x
-
Equation 11324*x%=211
- Equation x^3+6x^2-x-6=0
-
Equation x-4/3+x/2=5
- Express {x} in terms of y where:
- 2*x+3*y=5
- -10*x+15*y=-7
- -7*x-15*y=-8
- -8*x+6*y=-18
- Derivative of:
-
-x-1
- Graphing y =:
-
-x-1
- Canonical form:
- -x-1
-
Identical expressions
- sqrt(-4x- seven)=-x- one
- square root of ( minus 4x minus 7) equally minus x minus 1
- square root of ( minus 4x minus seven) equally minus x minus one
- √(-4x-7)=-x-1
- sqrt-4x-7=-x-1
-
Similar expressions
- sqrt(4x-7)=-x-1
- sqrt(-4x+7)=-x-1
- (1/(0.4*sqrt(2*pi)))*exp(-(((x-1)^2)/0.32))=0
- (17-x)-11/28=3/28
- sqrt(-4x-7)=+x-1
- sqrt(-4x-7)=-x+1
- 7x-38=78-(x-14)
- 64x^2-(x-1)^2=0
sqrt(-4x-7)=-x-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{- 4 x - 7} = - x - 1$$
$$\sqrt{- 4 x - 7} = - x - 1$$
We raise the equation sides to 2-th degree
$$- 4 x - 7 = \left(- x - 1\right)^{2}$$
$$- 4 x - 7 = x^{2} + 2 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} - 6 x - 8 = 0$$
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
$$a = -1$$
$$b = -6$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -4$$
$$x_{2} = -2$$
Because
$$\sqrt{- 4 x - 7} = - x - 1$$
and
$$\sqrt{- 4 x - 7} \geq 0$$
then
$$- x - 1 \geq 0$$
or
$$x \leq -1$$
$$-\infty < x$$
The final answer:
$$x_{1} = -4$$
$$x_{2} = -2$$
$$\sqrt{- 4 x - 7} = - x - 1$$
$$\sqrt{- 4 x - 7} = - x - 1$$
We raise the equation sides to 2-th degree
$$- 4 x - 7 = \left(- x - 1\right)^{2}$$
$$- 4 x - 7 = x^{2} + 2 x + 1$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} - 6 x - 8 = 0$$
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
$$a = -1$$
$$b = -6$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (-1) * (-8) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -4$$
$$x_{2} = -2$$
Because
$$\sqrt{- 4 x - 7} = - x - 1$$
and
$$\sqrt{- 4 x - 7} \geq 0$$
then
$$- x - 1 \geq 0$$
or
$$x \leq -1$$
$$-\infty < x$$
The final answer:
$$x_{1} = -4$$
$$x_{2} = -2$$
Sum and product of roots
[src]
sum
-4 - 2
$$-4 - 2$$
=
-6
$$-6$$
product
-4*(-2)
$$- -8$$
=
8
$$8$$
8