Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4(x-1)=2(2x-8)+12
-
Equation x^2-18=7*x
-
Equation (x-4)/4=(x+3)/7
- Equation 2*x+y=5
- Express {x} in terms of y where:
- 4*x+13*y=8
- 14*x+17*y=19
- 3*x-11*y=20
- -18*x-13*y=2
- Derivative of:
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7*x
- Graphing y =:
- 7*x
- Integral of d{x}:
- 7*x
-
Identical expressions
- x^ two - eighteen = seven *x
- x squared minus 18 equally 7 multiply by x
- x to the power of two minus eighteen equally seven multiply by x
- x2-18=7*x
- x²-18=7*x
- x to the power of 2-18=7*x
- x^2-18=7x
- x2-18=7x
-
Similar expressions
- -x=6-7(x-3)
- x^2+18=7*x
x^2-18=7*x 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
$$x^{2} - 18 = 7 x$$
to
$$- 7 x + \left(x^{2} - 18\right) = 0$$
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
$$a = 1$$
$$b = -7$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = -2$$
left part with negative sign.
The equation is transformed from
$$x^{2} - 18 = 7 x$$
to
$$- 7 x + \left(x^{2} - 18\right) = 0$$
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
$$a = 1$$
$$b = -7$$
$$c = -18$$
, 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
$$x_{1} = 9$$
$$x_{2} = -2$$
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
-2 + 9
$$-2 + 9$$
=
7
$$7$$
product
-2*9
$$- 18$$
=
-18
$$-18$$
-18
The graph