Mister Exam
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How to use it?
- Equation:
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Equation -(-y+4)+2*y+1=0
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Equation 11-5(2x+1)=41-9x
- Equation 2*x^2+50=0
- Express {x} in terms of y where:
- -16*x-20*y=-13
- 4*x+5*y=7
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Identical expressions
- x^ two - twelve *x- eighteen = zero
- x squared minus 12 multiply by x minus 18 equally 0
- x to the power of two minus twelve multiply by x minus eighteen equally zero
- x2-12*x-18=0
- x²-12*x-18=0
- x to the power of 2-12*x-18=0
- x^2-12x-18=0
- x2-12x-18=0
- x^2-12*x-18=O
-
Similar expressions
- x^2-12*x+18=0
- x^2+12*x-18=0
x^2-12*x-18=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 1$$
$$b = -12$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6 + 3 \sqrt{6}$$
$$x_{2} = 6 - 3 \sqrt{6}$$
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
$$a = 1$$
$$b = -12$$
$$c = -18$$
, then
D = b^2 - 4 * a * c =
(-12)^2 - 4 * (1) * (-18) = 216
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6 + 3 \sqrt{6}$$
$$x_{2} = 6 - 3 \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = -18$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -12$$
$$q = \frac{c}{a}$$
$$q = -18$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 12$$
$$x_{1} x_{2} = -18$$
Rapid solution
[src]
___ x1 = 6 - 3*\/ 6
$$x_{1} = 6 - 3 \sqrt{6}$$
___ x2 = 6 + 3*\/ 6
$$x_{2} = 6 + 3 \sqrt{6}$$
x2 = 6 + 3*sqrt(6)
Sum and product of roots
[src]
sum
___ ___ 6 - 3*\/ 6 + 6 + 3*\/ 6
$$\left(6 - 3 \sqrt{6}\right) + \left(6 + 3 \sqrt{6}\right)$$
=
12
$$12$$
product
/ ___\ / ___\ \6 - 3*\/ 6 /*\6 + 3*\/ 6 /
$$\left(6 - 3 \sqrt{6}\right) \left(6 + 3 \sqrt{6}\right)$$
=
-18
$$-18$$
-18