Mister exam

# (7-2x)*(9-2x)-35=0 equation

A equation with variable:

#### Numerical solution:

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### The solution

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(7 - 2*x)*(9 - 2*x) - 35 = 0
$$\left(7 - 2 x\right) \left(9 - 2 x\right) - 35 = 0$$
Detail solution
Expand the expression in the equation
$$\left(7 - 2 x\right) \left(9 - 2 x\right) - 35 = 0$$
We get the quadratic equation
$$4 x^{2} - 32 x + 28 = 0$$
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
$$a = 4$$
$$b = -32$$
$$c = 28$$
, then
D = b^2 - 4 * a * c =

(-32)^2 - 4 * (4) * (28) = 576

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 7$$
$$x_{2} = 1$$
The graph
Rapid solution [src]
x1 = 1
$$x_{1} = 1$$
x2 = 7
$$x_{2} = 7$$
x2 = 7
Sum and product of roots [src]
sum
1 + 7
$$1 + 7$$
=
8
$$8$$
product
7
$$7$$
=
7
$$7$$
7
Numerical answer [src]
x1 = 1.0
x2 = 7.0
x2 = 7.0
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