Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2^2-x-1=x^2-5*x-(-1-x^2)
-
Equation 0*x=0
-
Equation x^2=35
-
Equation 10*(x-9)=7
- Express {x} in terms of y where:
- -20*x-13*y=15
- 1*x-6*y=-19
- 7*x-2*y=20
- 18*x-12*y=-20
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
-
35
- Sum of series:
-
35
-
Identical expressions
- x^ two = thirty-five
- x squared equally 35
- x to the power of two equally thirty minus five
- x2=35
- x²=35
- x to the power of 2=35
-
Similar expressions
- sqrt(16-x^2)*(x^2-3*x-10)=0
- 3x^2-5x-2=0
- 3(5-2x)+4x=-7x
- d^4*y/((d*x^4))+9*d^3*y/((d*x^3))+21*d^2*y/((d*x^2))-d*y/(d*x)-30*y=0
- x^2+2x-24=0
- 3(5-x)+13=4(3x-8)
x^2=35 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
$$x^{2} = 35$$
to
$$x^{2} - 35 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -35$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{35}$$
$$x_{2} = - \sqrt{35}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 35$$
to
$$x^{2} - 35 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -35$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-35) = 140
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{35}$$
$$x_{2} = - \sqrt{35}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -35$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -35$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -35$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -35$$
Rapid solution
[src]
____ x1 = -\/ 35
$$x_{1} = - \sqrt{35}$$
____ x2 = \/ 35
$$x_{2} = \sqrt{35}$$
x2 = sqrt(35)
Sum and product of roots
[src]
sum
____ ____ - \/ 35 + \/ 35
$$- \sqrt{35} + \sqrt{35}$$
=
0
$$0$$
product
____ ____ -\/ 35 *\/ 35
$$- \sqrt{35} \sqrt{35}$$
=
-35
$$-35$$
-35
The graph