Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -20*(x-13)=-220
-
Equation x-x/12=55/12
-
Equation 3^x=81
-
Equation 12-x^2=11
- Express {x} in terms of y where:
- 18*x+19*y=7
- -10*x+13*y=5
- 16*x-15*y=4
- 1*x+6*y=6
- Graphing y =:
- 12-x^2
- Integral of d{x}:
- 12-x^2
-
11
- Sum of series:
-
11
- Derivative of:
- 11
-
Identical expressions
- twelve -x^ two = eleven
- 12 minus x squared equally 11
- twelve minus x to the power of two equally eleven
- 12-x2=11
- 12-x²=11
- 12-x to the power of 2=11
-
Similar expressions
- 12+x^2=11
12-x^2=11 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
$$12 - x^{2} = 11$$
to
$$\left(12 - x^{2}\right) - 11 = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = 1$$
left part with negative sign.
The equation is transformed from
$$12 - x^{2} = 11$$
to
$$\left(12 - x^{2}\right) - 11 = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (1) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = 1$$
Vieta's Theorem
rewrite the equation
$$12 - x^{2} = 11$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
$$12 - x^{2} = 11$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
The graph