Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x=2
-
Equation x^2+7x=18
-
Equation x^2-4x=0
-
Equation (y^4+4*y^2-12)/4=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- -7*x-19*y=-18
- 5*x+12*y=18
- -12*x-8*y=13
- Graphing y =:
- x^2+7x
- Derivative of:
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x^2+7x
-
18
- Integral of d{x}:
-
x^2+7x
- Sum of series:
-
18
- The double integral of:
- 18
-
Identical expressions
- x^ two +7x= eighteen
- x squared plus 7x equally 18
- x to the power of two plus 7x equally eighteen
- x2+7x=18
- x²+7x=18
- x to the power of 2+7x=18
-
Similar expressions
- x^2-7x=18
- (10*1*81*0.99*0.99*60)/27*x=71.78
x^2+7x=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
$$x^{2} + 7 x = 18$$
to
$$\left(x^{2} + 7 x\right) - 18 = 0$$
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
$$a = 1$$
$$b = 7$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -9$$
left part with negative sign.
The equation is transformed from
$$x^{2} + 7 x = 18$$
to
$$\left(x^{2} + 7 x\right) - 18 = 0$$
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 - it is the discriminant.
Because
$$a = 1$$
$$b = 7$$
$$c = -18$$
, then
D = b^2 - 4 * a * c =
(7)^2 - 4 * (1) * (-18) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -9$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = -18$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = -18$$
Sum and product of roots
[src]
sum
-9 + 2
$$-9 + 2$$
=
-7
$$-7$$
product
-9*2
$$- 18$$
=
-18
$$-18$$
-18
The graph