Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 49*x^3+14*x^2+x=0
-
Equation 4^x=8
-
Equation x^2-x=12
-
Equation x-5(x+3)=5
- Express {x} in terms of y where:
- -7*x-13*y=-12
- -3*x+19*y=16
- -4*x+4*y=-9
- -19*x-2*y=-6
- Graphing y =:
- x^2-x
- Derivative of:
-
x^2-x
- 12
- Integral of d{x}:
-
x^2-x
-
12
- Canonical form:
- 12
-
Identical expressions
- x^ two -x= twelve
- x squared minus x equally 12
- x to the power of two minus x equally twelve
- x2-x=12
- x²-x=12
- x to the power of 2-x=12
-
Similar expressions
- x^2+x=12
- x^2-x+y^2-y=0
- (-1-3x)^2-x(9x-2)=5
x^2-x=12 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
$$x^{2} - x = 12$$
to
$$\left(x^{2} - x\right) - 12 = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = -12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -3$$
left part with negative sign.
The equation is transformed from
$$x^{2} - x = 12$$
to
$$\left(x^{2} - x\right) - 12 = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-12) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -3$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -12$$
Sum and product of roots
[src]
sum
-3 + 4
$$-3 + 4$$
=
1
$$1$$
product
-3*4
$$- 12$$
=
-12
$$-12$$
-12
The graph