Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x)=0
-
Equation x^2=64
-
Equation z^3=1
-
Equation 2^x=-1
- Express {x} in terms of y where:
- -7*x+19*y=-8
- 5*x+8*y=6
- 6*x+14*y=-7
- 3*x+6*y=16
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
- Sum of series:
-
64
-
Identical expressions
- x^ two = sixty-four
- x squared equally 64
- x to the power of two equally sixty minus four
- x2=64
- x²=64
- x to the power of 2=64
-
Similar expressions
- x^2-9*x+14=0
x^2=64 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
$$x^{2} = 64$$
to
$$x^{2} - 64 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -64$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
$$x_{2} = -8$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 64$$
to
$$x^{2} - 64 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -64$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-64) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
$$x_{2} = -8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -64$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -64$$
$$p x + q + x^{2} = 0$$
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
-8 + 8
$$-8 + 8$$
=
0
$$0$$
product
-8*8
$$- 64$$
=
-64
$$-64$$
-64
The graph