Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+9=(x+9)^2
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation cos(x)=-1
-
Equation 9x-7=6x+14
- Express {x} in terms of y where:
- -1*x-20*y=-17
- 7*x+13*y=-13
- -13*x+7*y=11
- 9*x+18*y=3
- Graphing y =:
- x^2
- Derivative of:
-
x^2
-
10
- Integral of d{x}:
-
x^2
-
10
- Sum of series:
-
10
-
Identical expressions
- x^ two = ten
- x squared equally 10
- x to the power of two equally ten
- x2=10
- x²=10
- x to the power of 2=10
-
Similar expressions
- -0.25x^2+x-1=0
- x^2-5x+14=0
- 6x^4+23x^3+3x^2-32x+12=0
- sqrt(1-x^2)/x=-187/156
- lg^2(x^2)+lg(10*x)-6=0
x^2=10 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
$$x^{2} = 10$$
to
$$x^{2} - 10 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{10}$$
$$x_{2} = - \sqrt{10}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 10$$
to
$$x^{2} - 10 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-10) = 40
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{10}$$
$$x_{2} = - \sqrt{10}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -10$$
Rapid solution
[src]
____ x1 = -\/ 10
$$x_{1} = - \sqrt{10}$$
____ x2 = \/ 10
$$x_{2} = \sqrt{10}$$
x2 = sqrt(10)
Sum and product of roots
[src]
sum
____ ____ - \/ 10 + \/ 10
$$- \sqrt{10} + \sqrt{10}$$
=
0
$$0$$
product
____ ____ -\/ 10 *\/ 10
$$- \sqrt{10} \sqrt{10}$$
=
-10
$$-10$$
-10
The graph