Mister Exam
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- Equation:
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Equation x^2+11*x+30=0
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Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
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Equation (|3*x-9|)-(|x+2|)=7
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Equation 3(x-1)-6=0
- Express {x} in terms of y where:
- 15*x-2*y=14
- -12*x+12*y=8
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- Derivative of:
- 34x
-
Identical expressions
- 34x=(2x- five)4x- five (x- seven)
- 34x equally (2x minus 5)4x minus 5(x minus 7)
- 34x equally (2x minus five)4x minus five (x minus seven)
- 34x=2x-54x-5x-7
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Similar expressions
- 13*4^x-3^x+2=7*3^x+4^x+1
- 32^((x-14)/3)*(4^(x+2))^x=64
- 3(4x+8)+2(5x+3)=2(3x+10)+3(3x+15)
- 34x=(2x-5)4x+5(x-7)
- 34x=(2x-5)4x-5(x+7)
- 3*4^(x)+2*9^x-5*6x=0
- 34x=(2x+5)4x-5(x-7)
34x=(2x-5)4x-5(x-7) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
34*x = (2*x - 5)*4*x - 5*(x - 7)
$$34 x = x 4 \left(2 x - 5\right) - 5 \left(x - 7\right)$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$34 x = x 4 \left(2 x - 5\right) - 5 \left(x - 7\right)$$
to
$$34 x + \left(- x 4 \left(2 x - 5\right) + 5 \left(x - 7\right)\right) = 0$$
Expand the expression in the equation
$$34 x + \left(- x 4 \left(2 x - 5\right) + 5 \left(x - 7\right)\right) = 0$$
We get the quadratic equation
$$- 8 x^{2} + 59 x - 35 = 0$$
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
$$a = -8$$
$$b = 59$$
$$c = -35$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{59}{16} - \frac{\sqrt{2361}}{16}$$
$$x_{2} = \frac{\sqrt{2361}}{16} + \frac{59}{16}$$
left part with negative sign.
The equation is transformed from
$$34 x = x 4 \left(2 x - 5\right) - 5 \left(x - 7\right)$$
to
$$34 x + \left(- x 4 \left(2 x - 5\right) + 5 \left(x - 7\right)\right) = 0$$
Expand the expression in the equation
$$34 x + \left(- x 4 \left(2 x - 5\right) + 5 \left(x - 7\right)\right) = 0$$
We get the quadratic equation
$$- 8 x^{2} + 59 x - 35 = 0$$
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
$$a = -8$$
$$b = 59$$
$$c = -35$$
, then
D = b^2 - 4 * a * c =
(59)^2 - 4 * (-8) * (-35) = 2361
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{59}{16} - \frac{\sqrt{2361}}{16}$$
$$x_{2} = \frac{\sqrt{2361}}{16} + \frac{59}{16}$$
Sum and product of roots
[src]
sum
______ ______ 59 \/ 2361 59 \/ 2361 -- - -------- + -- + -------- 16 16 16 16
$$\left(\frac{59}{16} - \frac{\sqrt{2361}}{16}\right) + \left(\frac{\sqrt{2361}}{16} + \frac{59}{16}\right)$$
=
59/8
$$\frac{59}{8}$$
product
/ ______\ / ______\ |59 \/ 2361 | |59 \/ 2361 | |-- - --------|*|-- + --------| \16 16 / \16 16 /
$$\left(\frac{59}{16} - \frac{\sqrt{2361}}{16}\right) \left(\frac{\sqrt{2361}}{16} + \frac{59}{16}\right)$$
=
35/8
$$\frac{35}{8}$$
35/8
Rapid solution
[src]
______
59 \/ 2361
x1 = -- - --------
16 16
$$x_{1} = \frac{59}{16} - \frac{\sqrt{2361}}{16}$$
______
59 \/ 2361
x2 = -- + --------
16 16
$$x_{2} = \frac{\sqrt{2361}}{16} + \frac{59}{16}$$
x2 = sqrt(2361)/16 + 59/16