Mister Exam
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- Equation:
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Equation x^2+4*x+4=0
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Equation (x^2-4)^2+(x^2-3x-10)^2=0
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Equation -x/3+x+7=3
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Equation -20*(x-13)=-220
- Express {x} in terms of y where:
- -14*x+4*y=-16
- -13*x-10*y=5
- 9*x-1*y=17
- -12*x-8*y=13
- Factor squared:
- x^2+4*x+4
- Canonical form:
- x^2+4*x+4
- Factor polynomial:
- x^2+4*x+4
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Identical expressions
- x^ two + four *x+ four = zero
- x squared plus 4 multiply by x plus 4 equally 0
- x to the power of two plus four multiply by x plus four equally zero
- x2+4*x+4=0
- x²+4*x+4=0
- x to the power of 2+4*x+4=0
- x^2+4x+4=0
- x2+4x+4=0
- x^2+4*x+4=O
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Similar expressions
- x^2+4*x-4=0
- x^2-4*x+4=0
x^2+4*x+4=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
$$a = 1$$
$$b = 4$$
$$c = 4$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = -2$$
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
$$a = 1$$
$$b = 4$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (4) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -4/2/(1)
$$x_{1} = -2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 4$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 4$$
The graph