Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 12-(4-x)^2=x(3-x)
-
Equation 3^x=-3
-
Equation x^2-7*x+5=0
-
Equation (x+1)^2=0
- Express {x} in terms of y where:
- -11*x-14*y=6
- -17*x+9*y=-18
- 15*x+6*y=16
- 16*x-1*y=17
-
Identical expressions
- x^ two - thirty-six *x+ three hundred and twenty-four = zero
- x squared minus 36 multiply by x plus 324 equally 0
- x to the power of two minus thirty minus six multiply by x plus three hundred and twenty minus four equally zero
- x2-36*x+324=0
- x²-36*x+324=0
- x to the power of 2-36*x+324=0
- x^2-36x+324=0
- x2-36x+324=0
- x^2-36*x+324=O
-
Similar expressions
- x^2+36*x+324=0
- x^2-36*x-324=0
x^2-36*x+324=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 1$$
$$b = -36$$
$$c = 324$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = 18$$
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
$$a = 1$$
$$b = -36$$
$$c = 324$$
, then
D = b^2 - 4 * a * c =
(-36)^2 - 4 * (1) * (324) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --36/2/(1)
$$x_{1} = 18$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -36$$
$$q = \frac{c}{a}$$
$$q = 324$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 36$$
$$x_{1} x_{2} = 324$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -36$$
$$q = \frac{c}{a}$$
$$q = 324$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 36$$
$$x_{1} x_{2} = 324$$
The graph