Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x^4-81=0
-
Equation 600-(x-37)=417
-
Equation 7x^2+8-13x=8x-6
-
Equation cos(x/8+pi/4)=1
- Express {x} in terms of y where:
- -12*x+3*y=-9
- 14*x-16*y=14
- 9*x-18*y=6
- -10*x+18*y=6
- Integral of d{x}:
- 8x-6
-
Identical expressions
- 7x^ two + eight -13x=8x- six
- 7x squared plus 8 minus 13x equally 8x minus 6
- 7x to the power of two plus eight minus 13x equally 8x minus six
- 7x2+8-13x=8x-6
- 7x²+8-13x=8x-6
- 7x to the power of 2+8-13x=8x-6
-
Similar expressions
- 3*(8*x-6)=4*(6*x-4,5)
- 7x^2-8-13x=8x-6
- x^4-(1/2)*x^2+8*x-6*(3/16)=0
- -7*x^3-364x^2+738^x-60=0
- 7x^2+8+13x=8x-6
- x^3-12*x^2+48*x-64=0
- 7x^2+8-13x=8x+6
7x^2+8-13x=8x-6 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
$$- 13 x + \left(7 x^{2} + 8\right) = 8 x - 6$$
to
$$\left(6 - 8 x\right) + \left(- 13 x + \left(7 x^{2} + 8\right)\right) = 0$$
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
$$a = 7$$
$$b = -21$$
$$c = 14$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = 1$$
left part with negative sign.
The equation is transformed from
$$- 13 x + \left(7 x^{2} + 8\right) = 8 x - 6$$
to
$$\left(6 - 8 x\right) + \left(- 13 x + \left(7 x^{2} + 8\right)\right) = 0$$
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
$$a = 7$$
$$b = -21$$
$$c = 14$$
, then
D = b^2 - 4 * a * c =
(-21)^2 - 4 * (7) * (14) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = 1$$
Vieta's Theorem
rewrite the equation
$$- 13 x + \left(7 x^{2} + 8\right) = 8 x - 6$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 x + 2 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = 2$$
$$- 13 x + \left(7 x^{2} + 8\right) = 8 x - 6$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 x + 2 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = 2$$
The graph