Mister Exam
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- Equation:
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Equation 23x-10+5x^2=0
- Equation (x-9)(x-a)=x^2-4ax+b
- Equation а^-12×(-4а^7)^2
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Equation tgx=0
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Identical expressions
- (x- nine)(x-a)=x^ two -4ax+b
- (x minus 9)(x minus a) equally x squared minus 4ax plus b
- (x minus nine)(x minus a) equally x to the power of two minus 4ax plus b
- (x-9)(x-a)=x2-4ax+b
- x-9x-a=x2-4ax+b
- (x-9)(x-a)=x²-4ax+b
- (x-9)(x-a)=x to the power of 2-4ax+b
- x-9x-a=x^2-4ax+b
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Similar expressions
- (x-9)(x-a)=x^2-4ax-b
- (x-9)(x-a)=x^2+4ax+b
- (x-9)(x+a)=x^2-4ax+b
- (x+9)(x-a)=x^2-4ax+b
(x-9)(x-a)=x^2-4ax+b equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 (x - 9)*(x - a) = x - 4*a*x + b
$$\left(- a + x\right) \left(x - 9\right) = b + \left(- 4 a x + x^{2}\right)$$
Detail solution
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without b)
from left part to right part, we given:
$$\left(- a + x\right) \left(x - 9\right) + 9 = - 4 a x + b + x^{2} + 9$$
Move the summands with the unknown b
from the right part to the left part:
$$- b + \left(- a + x\right) \left(x - 9\right) + 9 = - 4 a x + x^{2} + 9$$
Divide both parts of the equation by (9 - b + (-9 + x)*(x - a))/b
We get the answer: b = -9*x + 9*a + 3*a*x
(x-9)*(x-a) = x^2-4*a*x+b
Expand brackets in the left part
x-9x-a = x^2-4*a*x+b
Looking for similar summands in the left part:
(-9 + x)*(x - a) = x^2-4*a*x+b
Move free summands (without b)
from left part to right part, we given:
$$\left(- a + x\right) \left(x - 9\right) + 9 = - 4 a x + b + x^{2} + 9$$
Move the summands with the unknown b
from the right part to the left part:
$$- b + \left(- a + x\right) \left(x - 9\right) + 9 = - 4 a x + x^{2} + 9$$
Divide both parts of the equation by (9 - b + (-9 + x)*(x - a))/b
b = 9 + x^2 - 4*a*x / ((9 - b + (-9 + x)*(x - a))/b)
We get the answer: b = -9*x + 9*a + 3*a*x
The graph
Sum and product of roots
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sum
-9*re(x) + 3*re(a*x) + 9*re(a) + I*(-9*im(x) + 3*im(a*x) + 9*im(a))
$$i \left(9 \operatorname{im}{\left(a\right)} - 9 \operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(a x\right)}\right) + 9 \operatorname{re}{\left(a\right)} - 9 \operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(a x\right)}$$
=
-9*re(x) + 3*re(a*x) + 9*re(a) + I*(-9*im(x) + 3*im(a*x) + 9*im(a))
$$i \left(9 \operatorname{im}{\left(a\right)} - 9 \operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(a x\right)}\right) + 9 \operatorname{re}{\left(a\right)} - 9 \operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(a x\right)}$$
product
-9*re(x) + 3*re(a*x) + 9*re(a) + I*(-9*im(x) + 3*im(a*x) + 9*im(a))
$$i \left(9 \operatorname{im}{\left(a\right)} - 9 \operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(a x\right)}\right) + 9 \operatorname{re}{\left(a\right)} - 9 \operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(a x\right)}$$
=
-9*re(x) + 3*re(a*x) + 9*re(a) + 3*I*(-3*im(x) + 3*im(a) + im(a*x))
$$3 i \left(3 \operatorname{im}{\left(a\right)} - 3 \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(a x\right)}\right) + 9 \operatorname{re}{\left(a\right)} - 9 \operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(a x\right)}$$
-9*re(x) + 3*re(a*x) + 9*re(a) + 3*i*(-3*im(x) + 3*im(a) + im(a*x))
Rapid solution
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b1 = -9*re(x) + 3*re(a*x) + 9*re(a) + I*(-9*im(x) + 3*im(a*x) + 9*im(a))
$$b_{1} = i \left(9 \operatorname{im}{\left(a\right)} - 9 \operatorname{im}{\left(x\right)} + 3 \operatorname{im}{\left(a x\right)}\right) + 9 \operatorname{re}{\left(a\right)} - 9 \operatorname{re}{\left(x\right)} + 3 \operatorname{re}{\left(a x\right)}$$
b1 = i*(9*im(a) - 9*im(x) + 3*im(a*x)) + 9*re(a) - 9*re(x) + 3*re(a*x)