Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-87)-27=36
-
Equation x^3+2*x^2-9*x-18=0
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Equation 5*x^2=35*x
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Equation 4*(x-8)=-5
- Express {x} in terms of y where:
- 8*x-16*y=14
- -17*x-8*y=7
- -3*x-20*y=-13
- 15*x-3*y=19
- Derivative of:
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5*x^2
- Limit of the function:
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5*x^2
-
Identical expressions
- five *x^ two = thirty-five *x
- 5 multiply by x squared equally 35 multiply by x
- five multiply by x to the power of two equally thirty minus five multiply by x
- 5*x2=35*x
- 5*x²=35*x
- 5*x to the power of 2=35*x
- 5x^2=35x
- 5x2=35x
-
Similar expressions
- x^4-35x^2-36=0
- -18x-29=35x-29
- log(1/3)*(5*x2+x-15)=log(1/3)*(x-10)
- 0,3(5x-7)=3(0,2x+3,2)
- 5*x^2-4=0
5*x^2=35*x 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
$$5 x^{2} = 35 x$$
to
$$5 x^{2} - 35 x = 0$$
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
$$a = 5$$
$$b = -35$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = 0$$
left part with negative sign.
The equation is transformed from
$$5 x^{2} = 35 x$$
to
$$5 x^{2} - 35 x = 0$$
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
$$a = 5$$
$$b = -35$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-35)^2 - 4 * (5) * (0) = 1225
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = 0$$
Vieta's Theorem
rewrite the equation
$$5 x^{2} = 35 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 7 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 0$$
$$5 x^{2} = 35 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 7 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = 0$$
The graph