Mister Exam
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How to use it?
- Equation:
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Equation 5(x+9)=-8
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Equation 1/x=0
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Equation sin((2*x+2*pi)/3)*cos((4*x+pi)/3)-cos(2*x)=sin(x)^2/cos(-(-pi)/3)
- Equation x+3=√(2x^2+18)
- Express {x} in terms of y where:
- 10*x-1*y=10
- 17*x+16*y=7
- 17*x-11*y=2
- -12*x+3*y=-9
- Graphing y =:
-
x+3
- Inequation:
- x+3
- Canonical form:
- x+3
-
Identical expressions
- x+ three =√(two x^2+ eighteen)
- x plus 3 equally √(2x squared plus 18)
- x plus three equally √(two x squared plus eighteen)
- x+3=√(2x2+18)
- x+3=√2x2+18
- x+3=√(2x²+18)
- x+3=√(2x to the power of 2+18)
- x+3=√2x^2+18
-
Similar expressions
- x-3=√(2x^2+18)
- x+3=√(2x^2-18)
- sin(x+(3pi/4))=0
- x+((3x-9)/5)=11-((15x-12)/3)
x+3=√(2x^2+18) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$x + 3 = \sqrt{2 x^{2} + 18}$$
Transfer the right side of the equation left part with negative sign
$$- \sqrt{2 x^{2} + 18} = - x - 3$$
We raise the equation sides to 2-th degree
$$2 x^{2} + 18 = \left(- x - 3\right)^{2}$$
$$2 x^{2} + 18 = x^{2} + 6 x + 9$$
Transfer the right side of the equation left part with negative sign
$$x^{2} - 6 x + 9 = 0$$
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
$$a = 1$$
$$b = -6$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = 3$$
Because
$$\sqrt{2 x^{2} + 18} = x + 3$$
and
$$\sqrt{2 x^{2} + 18} \geq 0$$
then
$$x + 3 \geq 0$$
or
$$-3 \leq x$$
$$x < \infty$$
The final answer:
$$x_{1} = 3$$
$$x + 3 = \sqrt{2 x^{2} + 18}$$
Transfer the right side of the equation left part with negative sign
$$- \sqrt{2 x^{2} + 18} = - x - 3$$
We raise the equation sides to 2-th degree
$$2 x^{2} + 18 = \left(- x - 3\right)^{2}$$
$$2 x^{2} + 18 = x^{2} + 6 x + 9$$
Transfer the right side of the equation left part with negative sign
$$x^{2} - 6 x + 9 = 0$$
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
$$a = 1$$
$$b = -6$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (9) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --6/2/(1)
$$x_{1} = 3$$
Because
$$\sqrt{2 x^{2} + 18} = x + 3$$
and
$$\sqrt{2 x^{2} + 18} \geq 0$$
then
$$x + 3 \geq 0$$
or
$$-3 \leq x$$
$$x < \infty$$
The final answer:
$$x_{1} = 3$$
Numerical answer
[src]
x1 = 3.00000206236079
x2 = 3.00000207223341
x3 = 3.00000203057035
x4 = 3.00000175923222
x5 = 3.00000208402891
x6 = 3.00000206501338
x7 = 3.00000187446746
x8 = 3.00000193921084
x9 = 3.00000196197755
x10 = 2.99999956207981
x11 = 3.00000206753704
x12 = 3.00000043646288
x13 = 3.0000019717504
x14 = 3.00000192584347
x15 = 3.00000199622178
x16 = 3.00000206994094
x17 = 3.00000191082803
x18 = 3.00000200308346
x19 = 3.00000203500952
x20 = 3.00000202582678
x21 = 3.00000208043071
x22 = 3.00000119292563
x23 = 3.00000205662719
x24 = 3.00000185216979
x25 = 2.99999629454227
x26 = 3.0000019806427
x27 = 3.00000200942096
x28 = 3.00000203917264
x29 = 3.0000020535225
x30 = 3.00000159016674
x31 = 3.00000149853047
x32 = 3.00000208226719
x33 = 3.00000207651365
x34 = 3.00000207851463
x35 = 3.00000091361568
x36 = 3.00000171493196
x37 = 3.00000205956914
x38 = 3.00000201529207
x39 = 3.0000017957004
x40 = 3.000001373332
x41 = 3.00000204308469
x42 = 3.00000182623514
x43 = 3.00000204676768
x44 = 3.00000207442201
x45 = 3.00000205024116
x46 = 3.00000198876817
x47 = 3.00000208572037
x48 = 2.99999798006566
x49 = 3.0000016600044
x50 = 3.0000020207464
x51 = 3.00000195118682
x52 = 3.00000189384076
x52 = 3.00000189384076