Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 8*x=56
-
Equation 2−3(7+2x)=11
- Equation z^6+64=0
-
Equation 3x^2-4x-4=0
- Express {x} in terms of y where:
- -14*x+12*y=-18
- -14*x+9*y=-17
- -16*x-18*y=17
- 1*x+5*y=-7
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- 8x(one +2x)=- one
- 8x(1 plus 2x) equally minus 1
- 8x(one plus 2x) equally minus one
- 8x1+2x=-1
-
Similar expressions
- 8x(1+2x)=+1
- 8x(1-2x)=-1
- y=100+38*x1+2*x12+51*x2+51*x22+20*x1*x2
8x(1+2x)=-1 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
$$8 x \left(2 x + 1\right) = -1$$
to
$$8 x \left(2 x + 1\right) + 1 = 0$$
Expand the expression in the equation
$$8 x \left(2 x + 1\right) + 1 = 0$$
We get the quadratic equation
$$16 x^{2} + 8 x + 1 = 0$$
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
$$a = 16$$
$$b = 8$$
$$c = 1$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = - \frac{1}{4}$$
left part with negative sign.
The equation is transformed from
$$8 x \left(2 x + 1\right) = -1$$
to
$$8 x \left(2 x + 1\right) + 1 = 0$$
Expand the expression in the equation
$$8 x \left(2 x + 1\right) + 1 = 0$$
We get the quadratic equation
$$16 x^{2} + 8 x + 1 = 0$$
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
$$a = 16$$
$$b = 8$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(8)^2 - 4 * (16) * (1) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -8/2/(16)
$$x_{1} = - \frac{1}{4}$$
Sum and product of roots
[src]
sum
-1/4
$$- \frac{1}{4}$$
=
-1/4
$$- \frac{1}{4}$$
product
-1/4
$$- \frac{1}{4}$$
=
-1/4
$$- \frac{1}{4}$$
-1/4
The graph