Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation -x²=-67x
- Equation X÷4=20×2
-
Equation sin(4*x)=-sqrt(2)/2
-
Equation x-180=6688/19
- Express {x} in terms of y where:
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- (x^2+y^2-1)^3+x^2*y^3=0
- Canonical form:
- -x²
- Graphing y =:
- -x²
-
Identical expressions
- -x²=-67x
- minus x² equally minus 67x
-
Similar expressions
- 9*(3*x+6)-6*(7*x-14)-2*(x+1)=0
- (7-x)²-(x-16)²=0
- x^2-67*x+405=0
- (x+10)²=(5-x)²
- 7^(2x)-6*7^(x)+5=0
- -x^3-67*x+12=0
- -x²=+67x
- x²=-67x
-x²=-67x 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
$$- x^{2} = - 67 x$$
to
$$- x^{2} + 67 x = 0$$
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
$$a = -1$$
$$b = 67$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 67$$
left part with negative sign.
The equation is transformed from
$$- x^{2} = - 67 x$$
to
$$- x^{2} + 67 x = 0$$
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
$$a = -1$$
$$b = 67$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(67)^2 - 4 * (-1) * (0) = 4489
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 67$$
Vieta's Theorem
rewrite the equation
$$- x^{2} = - 67 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 67 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -67$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 67$$
$$x_{1} x_{2} = 0$$
$$- x^{2} = - 67 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 67 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -67$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 67$$
$$x_{1} x_{2} = 0$$