Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4x+7=0
-
Equation x*log(x)=0
-
Equation (x+10)(-x-8)=0
-
Equation x^2-4x=18
- Express {x} in terms of y where:
- 14*x-16*y=-3
- 17*x-20*y=6
- 10*x-19*y=3
- -2*x-1*y=-8
- Integral of d{x}:
-
x^2-4x
- Graphing y =:
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x^2-4x
- Canonical form:
- x^2-4x
- Sum of series:
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18
- Derivative of:
-
18
- The double integral of:
- 18
-
Identical expressions
- x^ two -4x= eighteen
- x squared minus 4x equally 18
- x to the power of two minus 4x equally eighteen
- x2-4x=18
- x²-4x=18
- x to the power of 2-4x=18
-
Similar expressions
- 3*x^2-4*x=0
- x^2-4*x-6=0
- 3x^2-4x+1
- x^2+4x=18
- logx-1(8)=1
- x^2-4x-2√(3x^2+14x-11)-1=0
x^2-4x=18 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
$$x^{2} - 4 x = 18$$
to
$$\left(x^{2} - 4 x\right) - 18 = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -4$$
$$c = -18$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-4\right)^{2} - 1 \cdot 4 \left(-18\right) = 88$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 2 + \sqrt{22}$$
Simplify
$$x_{2} = - \sqrt{22} + 2$$
Simplify
left part with negative sign.
The equation is transformed from
$$x^{2} - 4 x = 18$$
to
$$\left(x^{2} - 4 x\right) - 18 = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -4$$
$$c = -18$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-4\right)^{2} - 1 \cdot 4 \left(-18\right) = 88$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 2 + \sqrt{22}$$
Simplify
$$x_{2} = - \sqrt{22} + 2$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -18$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -18$$
Rapid solution
[src]
____ x_1 = 2 - \/ 22
$$x_{1} = - \sqrt{22} + 2$$
____ x_2 = 2 + \/ 22
$$x_{2} = 2 + \sqrt{22}$$
Sum and product of roots
[src]
sum
____ ____ 2 - \/ 22 + 2 + \/ 22
$$\left(- \sqrt{22} + 2\right) + \left(2 + \sqrt{22}\right)$$
=
4
$$4$$
product
____ ____ 2 - \/ 22 * 2 + \/ 22
$$\left(- \sqrt{22} + 2\right) * \left(2 + \sqrt{22}\right)$$
=
-18
$$-18$$
The graph