Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3*x/3=(1-x)/2
-
Equation tan(x)=-5
-
Equation sqrt(x-2)=x-4
-
Equation 32*x=2
- Express {x} in terms of y where:
- -13*x+15*y=1
- 11*x-6*y=-1
- -8*x-15*y=-12
- 18*x-15*y=-7
- Derivative of:
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sqrt(5x-1)
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x-5
- Integral of d{x}:
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sqrt(5x-1)
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x-5
- Graphing y =:
- x-5
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Identical expressions
- sqrt(five x- one)=x-5
- square root of (5x minus 1) equally x minus 5
- square root of (five x minus one) equally x minus 5
- √(5x-1)=x-5
- sqrt5x-1=x-5
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Similar expressions
- sqrt(5x-1)=x+5
- sqrt(5x+2)-sqrt(5x-10)=2
- sqrt(5x-16)=3
- sqrt(5x+1)=x-5
- 3*cos(2*x)-5*sin(x)+1=0
sqrt(5x-1)=x-5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{5 x - 1} = x - 5$$
$$\sqrt{5 x - 1} = x - 5$$
We raise the equation sides to 2-th degree
$$5 x - 1 = \left(x - 5\right)^{2}$$
$$5 x - 1 = x^{2} - 10 x + 25$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 15 x - 26 = 0$$
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
$$a = -1$$
$$b = 15$$
$$c = -26$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = 13$$
Because
$$\sqrt{5 x - 1} = x - 5$$
and
$$\sqrt{5 x - 1} \geq 0$$
then
$$x - 5 \geq 0$$
or
$$5 \leq x$$
$$x < \infty$$
The final answer:
$$x_{2} = 13$$
$$\sqrt{5 x - 1} = x - 5$$
$$\sqrt{5 x - 1} = x - 5$$
We raise the equation sides to 2-th degree
$$5 x - 1 = \left(x - 5\right)^{2}$$
$$5 x - 1 = x^{2} - 10 x + 25$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} + 15 x - 26 = 0$$
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
$$a = -1$$
$$b = 15$$
$$c = -26$$
, then
D = b^2 - 4 * a * c =
(15)^2 - 4 * (-1) * (-26) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = 13$$
Because
$$\sqrt{5 x - 1} = x - 5$$
and
$$\sqrt{5 x - 1} \geq 0$$
then
$$x - 5 \geq 0$$
or
$$5 \leq x$$
$$x < \infty$$
The final answer:
$$x_{2} = 13$$