Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 6x-2x+1=5
-
Equation 2x-4=8+2x
-
Equation x^4-2*x^2-15=0
-
Equation 3^x=-1
- Express {x} in terms of y where:
- -11*x+10*y=-3
- -10*x+13*y=5
- 10*x-6*y=9
- -4*x+14*y=-2
-
Identical expressions
- one / two x^2- thirty-two = zero
- 1 divide by 2x squared minus 32 equally 0
- one divide by two x squared minus thirty minus two equally zero
- 1/2x2-32=0
- 1/2x²-32=0
- 1/2x to the power of 2-32=0
- 1/2x^2-32=O
- 1 divide by 2x^2-32=0
-
Similar expressions
- 1/2x^2+32=0
1/2x^2-32=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(\frac{x^{2}}{2} - 32\right) + 0 = 0$$
We get the quadratic equation
$$\frac{x^{2}}{2} - 32 = 0$$
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
$$a = \frac{1}{2}$$
$$b = 0$$
$$c = -32$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
Simplify
$$x_{2} = -8$$
Simplify
$$\left(\frac{x^{2}}{2} - 32\right) + 0 = 0$$
We get the quadratic equation
$$\frac{x^{2}}{2} - 32 = 0$$
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
$$a = \frac{1}{2}$$
$$b = 0$$
$$c = -32$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1/2) * (-32) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
Simplify
$$x_{2} = -8$$
Simplify
Vieta's Theorem
rewrite the equation
$$\frac{x^{2}}{2} - 32 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 64 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -64$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -64$$
$$\frac{x^{2}}{2} - 32 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 64 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -64$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -64$$
Sum and product of roots
[src]
sum
0 - 8 + 8
$$\left(-8 + 0\right) + 8$$
=
0
$$0$$
product
1*-8*8
$$1 \left(-8\right) 8$$
=
-64
$$-64$$
-64
The graph