Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+2)^4-4*(x+2)^2-5=0
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Derivative of:
-
x^2+x
- 12
- Integral of d{x}:
-
x^2+x
-
12
- Canonical form:
- x^2+x
- 12
-
Identical expressions
- x^ two +x= twelve
- x squared plus x equally 12
- x to the power of two plus x equally twelve
- x2+x=12
- x²+x=12
- x to the power of 2+x=12
-
Similar expressions
- -2*x^4/(x^2-1)^2+3*x^2/(x^2-1)=0
- x^2-x=12
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
$$x_{1} = 3$$
$$x_{2} = -4$$
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
$$x_{1} = 3$$
$$x_{2} = -4$$
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
-4 + 3
$$-4 + 3$$
=
-1
$$-1$$
product
-4*3
$$- 12$$
=
-12
$$-12$$
-12
The graph