Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2-2=0
-
Equation x+(x*3)=168
- Equation x-1=1+(1/2)*y
-
Equation -4+x/5=x+4/2
- Express {x} in terms of y where:
- 15*x+2*y=8
- 1*x+4*y=-11
- 5*x-18*y=-17
- -9*x+6*y=18
- Sum of series:
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25
- Integral of d{x}:
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25
- Canonical form:
- 25
-
Identical expressions
- (2x- three)(2x- three)= twenty-five
- (2x minus 3)(2x minus 3) equally 25
- (2x minus three)(2x minus three) equally twenty minus five
- 2x-32x-3=25
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Similar expressions
- (2x-3)(2x+3)=25
- 2^x-3*2^x-3=40
- (2x+3)(2x-3)=25
(2x-3)(2x-3)=25 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
$$\left(2 x - 3\right) \left(2 x - 3\right) = 25$$
to
$$\left(2 x - 3\right) \left(2 x - 3\right) - 25 = 0$$
Expand the expression in the equation
$$\left(2 x - 3\right) \left(2 x - 3\right) - 25 = 0$$
We get the quadratic equation
$$4 x^{2} - 12 x - 16 = 0$$
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
$$a = 4$$
$$b = -12$$
$$c = -16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -1$$
left part with negative sign.
The equation is transformed from
$$\left(2 x - 3\right) \left(2 x - 3\right) = 25$$
to
$$\left(2 x - 3\right) \left(2 x - 3\right) - 25 = 0$$
Expand the expression in the equation
$$\left(2 x - 3\right) \left(2 x - 3\right) - 25 = 0$$
We get the quadratic equation
$$4 x^{2} - 12 x - 16 = 0$$
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
$$a = 4$$
$$b = -12$$
$$c = -16$$
, then
D = b^2 - 4 * a * c =
(-12)^2 - 4 * (4) * (-16) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -1$$