Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-8=(x-4)^2
-
Equation 2,6x-0,75=0,9x-35,6
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Equation (x+3)/3=(3-x)/8
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Equation 36-x^2=0
- Express {x} in terms of y where:
- 8*x+5*y=-12
- -7*x-4*y=-4
- -2*x-10*y=20
- -1*x+11*y=16
- Factor polynomial:
- 36-x^2
-
Identical expressions
- thirty-six -x^ two = zero
- 36 minus x squared equally 0
- thirty minus six minus x to the power of two equally zero
- 36-x2=0
- 36-x²=0
- 36-x to the power of 2=0
- 36-x^2=O
-
Similar expressions
- 36+x^2=0
36-x^2=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
$$a = -1$$
$$b = 0$$
$$c = 36$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -6$$
$$x_{2} = 6$$
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
$$a = -1$$
$$b = 0$$
$$c = 36$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (36) = 144
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -6$$
$$x_{2} = 6$$
Vieta's Theorem
rewrite the equation
$$36 - x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 36 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -36$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -36$$
$$36 - x^{2} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 36 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -36$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -36$$
Sum and product of roots
[src]
sum
-6 + 6
$$-6 + 6$$
=
0
$$0$$
product
-6*6
$$- 36$$
=
-36
$$-36$$
-36
The graph