Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x=25
-
Equation x^3=5
-
Equation 2x=4
-
Equation x^2=x+72
- Express {x} in terms of y where:
- 11*x+3*y=-16
- -2*x+13*y=-6
- 20*x-3*y=3
- 18*x-7*y=-4
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
-
Identical expressions
- x^ two =x+ seventy-two
- x squared equally x plus 72
- x to the power of two equally x plus seventy minus two
- x2=x+72
- x²=x+72
- x to the power of 2=x+72
-
Similar expressions
- x^2=x-72
- x^2-4|x|+8x=0
- (x+7)^2-(x-4)(x+4)=65
- x^2-9*x+14=0
- -2x^2-7x+19=(x+7)^2
x^2=x+72 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
$$x^{2} = x + 72$$
to
$$x^{2} + \left(- x - 72\right) = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = -72$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = -8$$
left part with negative sign.
The equation is transformed from
$$x^{2} = x + 72$$
to
$$x^{2} + \left(- x - 72\right) = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = -72$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-72) = 289
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
$$x_{2} = -8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -72$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -72$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -72$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -72$$
Sum and product of roots
[src]
sum
-8 + 9
$$-8 + 9$$
=
1
$$1$$
product
-8*9
$$- 72$$
=
-72
$$-72$$
-72
The graph