Mister Exam
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How to use it?
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Equation 32*x=2
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Identical expressions
- (- four x+ two)^ two =4
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Similar expressions
- (4x+2)^2=4
- (-4x-2)^2=4
(-4x+2)^2=4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(2 - 4 x\right)^{2} = 4$$
to
$$\left(2 - 4 x\right)^{2} - 4 = 0$$
Expand the expression in the equation
$$\left(2 - 4 x\right)^{2} - 4 = 0$$
We get the quadratic equation
$$16 x^{2} - 16 x = 0$$
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
$$a = 16$$
$$b = -16$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = 0$$
left part with negative sign.
The equation is transformed from
$$\left(2 - 4 x\right)^{2} = 4$$
to
$$\left(2 - 4 x\right)^{2} - 4 = 0$$
Expand the expression in the equation
$$\left(2 - 4 x\right)^{2} - 4 = 0$$
We get the quadratic equation
$$16 x^{2} - 16 x = 0$$
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
$$a = 16$$
$$b = -16$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-16)^2 - 4 * (16) * (0) = 256
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = 0$$