Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+9=(x+9)^2
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Equation cos(x)=-1
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Equation 3*x+50=77
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Equation 5-2(x-1)=4-x
- Express {x} in terms of y where:
- 10*x+5*y=-17
- 14*x+16*y=-3
- -19*x+1*y=0
- 9*x-4*y=2
- Integral of d{x}:
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1,5
- Sum of series:
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1,5
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Identical expressions
- (three hundred and seventy-six - one 8x)(two hundred -14x)=1, five
- (376 minus 18x)(200 minus 14x) equally 1,5
- (three hundred and seventy minus six minus one 8x)(two hundred minus 14x) equally 1, five
- 376-18x200-14x=1,5
-
Similar expressions
- (376-18x)(200+14x)=1,5
- (376+18x)(200-14x)=1,5
(376-18x)(200-14x)=1,5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
(376 - 18*x)*(200 - 14*x) = 3/2
$$\left(200 - 14 x\right) \left(376 - 18 x\right) = \frac{3}{2}$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(200 - 14 x\right) \left(376 - 18 x\right) = \frac{3}{2}$$
to
$$\left(200 - 14 x\right) \left(376 - 18 x\right) - \frac{3}{2} = 0$$
Expand the expression in the equation
$$\left(200 - 14 x\right) \left(376 - 18 x\right) - \frac{3}{2} = 0$$
We get the quadratic equation
$$252 x^{2} - 8864 x + \frac{150397}{2} = 0$$
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
$$a = 252$$
$$b = -8864$$
$$c = \frac{150397}{2}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{\sqrt{692602}}{252} + \frac{1108}{63}$$
$$x_{2} = \frac{1108}{63} - \frac{\sqrt{692602}}{252}$$
left part with negative sign.
The equation is transformed from
$$\left(200 - 14 x\right) \left(376 - 18 x\right) = \frac{3}{2}$$
to
$$\left(200 - 14 x\right) \left(376 - 18 x\right) - \frac{3}{2} = 0$$
Expand the expression in the equation
$$\left(200 - 14 x\right) \left(376 - 18 x\right) - \frac{3}{2} = 0$$
We get the quadratic equation
$$252 x^{2} - 8864 x + \frac{150397}{2} = 0$$
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
$$a = 252$$
$$b = -8864$$
$$c = \frac{150397}{2}$$
, then
D = b^2 - 4 * a * c =
(-8864)^2 - 4 * (252) * (150397/2) = 2770408
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{\sqrt{692602}}{252} + \frac{1108}{63}$$
$$x_{2} = \frac{1108}{63} - \frac{\sqrt{692602}}{252}$$
Sum and product of roots
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sum
________ ________ 1108 \/ 692602 1108 \/ 692602 ---- - ---------- + ---- + ---------- 63 252 63 252
$$\left(\frac{1108}{63} - \frac{\sqrt{692602}}{252}\right) + \left(\frac{\sqrt{692602}}{252} + \frac{1108}{63}\right)$$
=
2216 ---- 63
$$\frac{2216}{63}$$
product
/ ________\ / ________\ |1108 \/ 692602 | |1108 \/ 692602 | |---- - ----------|*|---- + ----------| \ 63 252 / \ 63 252 /
$$\left(\frac{1108}{63} - \frac{\sqrt{692602}}{252}\right) \left(\frac{\sqrt{692602}}{252} + \frac{1108}{63}\right)$$
=
150397 ------ 504
$$\frac{150397}{504}$$
150397/504
Rapid solution
[src]
________
1108 \/ 692602
x1 = ---- - ----------
63 252
$$x_{1} = \frac{1108}{63} - \frac{\sqrt{692602}}{252}$$
________
1108 \/ 692602
x2 = ---- + ----------
63 252
$$x_{2} = \frac{\sqrt{692602}}{252} + \frac{1108}{63}$$
x2 = sqrt(692602)/252 + 1108/63