Mister Exam
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How to use it?
- Equation:
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Equation x^2=11
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Equation (x+2)^4+(x+2)^2-12=0
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Identical expressions
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Similar expressions
- 2*(10x-9)^2+8*(10x-9)+8=0
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- 2*(10x-9)^2-8*(10x+9)+8=0
2*(10x-9)^2-8*(10x-9)+8=0 equation
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The solution
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[src]
2 2*(10*x - 9) - 8*(10*x - 9) + 8 = 0
$$2 \left(10 x - 9\right)^{2} - 8 \cdot \left(10 x - 9\right) + 8 = 0$$
Detail solution
Expand the expression in the equation
$$\left(2 \left(10 x - 9\right)^{2} - 8 \cdot \left(10 x - 9\right) + 8\right) + 0 = 0$$
We get the quadratic equation
$$200 x^{2} - 440 x + 242 = 0$$
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
$$a = 200$$
$$b = -440$$
$$c = 242$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = \frac{11}{10}$$
$$\left(2 \left(10 x - 9\right)^{2} - 8 \cdot \left(10 x - 9\right) + 8\right) + 0 = 0$$
We get the quadratic equation
$$200 x^{2} - 440 x + 242 = 0$$
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
$$a = 200$$
$$b = -440$$
$$c = 242$$
, then
D = b^2 - 4 * a * c =
(-440)^2 - 4 * (200) * (242) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --440/2/(200)
$$x_{1} = \frac{11}{10}$$
Sum and product of roots
[src]
sum
11
0 + --
10
$$0 + \frac{11}{10}$$
=
11 -- 10
$$\frac{11}{10}$$
product
11 1*-- 10
$$1 \cdot \frac{11}{10}$$
=
11 -- 10
$$\frac{11}{10}$$
11/10
The graph