Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 1,6(x+0,78)=4,64
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Equation x^2-4x-21=0
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Equation x^3-x^2-x+2=0
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Equation x*(x+5)=0
- Express {x} in terms of y where:
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Identical expressions
- six ^ two =x(x+ five)
- 6 squared equally x(x plus 5)
- six to the power of two equally x(x plus five)
- 62=x(x+5)
- 62=xx+5
- 6²=x(x+5)
- 6 to the power of 2=x(x+5)
- 6^2=xx+5
-
Similar expressions
- 6^2=x(x-5)
- 72=(100x(x+50))/2*50^2
- x*(x+5)=0
6^2=x(x+5) 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
$$36 = x \left(x + 5\right)$$
to
$$- x \left(x + 5\right) + 36 = 0$$
Expand the expression in the equation
$$- x \left(x + 5\right) + 36 = 0$$
We get the quadratic equation
$$- x^{2} - 5 x + 36 = 0$$
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
$$a = -1$$
$$b = -5$$
$$c = 36$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -9$$
$$x_{2} = 4$$
left part with negative sign.
The equation is transformed from
$$36 = x \left(x + 5\right)$$
to
$$- x \left(x + 5\right) + 36 = 0$$
Expand the expression in the equation
$$- x \left(x + 5\right) + 36 = 0$$
We get the quadratic equation
$$- x^{2} - 5 x + 36 = 0$$
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
$$a = -1$$
$$b = -5$$
$$c = 36$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (-1) * (36) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -9$$
$$x_{2} = 4$$
Sum and product of roots
[src]
sum
-9 + 4
$$-9 + 4$$
=
-5
$$-5$$
product
-9*4
$$- 36$$
=
-36
$$-36$$
-36