Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+2x+1=0
-
Equation cos(x/2)=1/2
-
Equation (x+7)*(x-1)=0
-
Equation -4/7*x^2+28=0
- Express {x} in terms of y where:
- -17*x+14*y=11
- -1*x-17*y=10
- 3*x+3*y=10
- 12*x+12*y=-3
-
Identical expressions
- - three * zero , three thousand, nine hundred and four *x^ two - zero , eight hundred and eighty-eight * two *x+ six , six thousand, nine hundred and thirty-two = zero
- minus 3 multiply by 0,3904 multiply by x squared minus 0,888 multiply by 2 multiply by x plus 6,6932 equally 0
- minus three multiply by zero , three thousand, nine hundred and four multiply by x to the power of two minus zero , eight hundred and eighty minus eight multiply by two multiply by x plus six , six thousand, nine hundred and thirty minus two equally zero
- -3*0,3904*x2-0,888*2*x+6,6932=0
- -3*0,3904*x²-0,888*2*x+6,6932=0
- -3*0,3904*x to the power of 2-0,888*2*x+6,6932=0
- -30,3904x^2-0,8882x+6,6932=0
- -30,3904x2-0,8882x+6,6932=0
- -3*0,3904*x^2-0,888*2*x+6,6932=O
-
Similar expressions
- -3*0,3904*x^2+0,888*2*x+6,6932=0
- -3*0,3904*x^2-0,888*2*x-6,6932=0
- 3*0,3904*x^2-0,888*2*x+6,6932=0
-3*0,3904*x^2-0,888*2*x+6,6932=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 111*2
- 1.1712*x - -----*x + 6.6932 = 0
125
$$\left(- 1.1712 x^{2} - \frac{2 \cdot 111}{125} x\right) + 6.6932 = 0$$
Detail solution
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
$$a = -1.1712$$
$$b = - \frac{222}{125}$$
$$c = 6.6932$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3.26612109668228$$
$$x_{2} = 1.74972765405933$$
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
$$a = -1.1712$$
$$b = - \frac{222}{125}$$
$$c = 6.6932$$
, then
D = b^2 - 4 * a * c =
(-222/125)^2 - 4 * (-1.1712) * (6.6932) = 34.5104793600000
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3.26612109668228$$
$$x_{2} = 1.74972765405933$$
Vieta's Theorem
rewrite the equation
$$\left(- 1.1712 x^{2} - \frac{2 \cdot 111}{125} x\right) + 6.6932 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$1 x^{2} + 1.51639344262295 x - 5.71482240437158 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1.51639344262295$$
$$q = \frac{c}{a}$$
$$q = -5.71482240437158$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1.51639344262295$$
$$x_{1} x_{2} = -5.71482240437158$$
$$\left(- 1.1712 x^{2} - \frac{2 \cdot 111}{125} x\right) + 6.6932 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$1 x^{2} + 1.51639344262295 x - 5.71482240437158 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1.51639344262295$$
$$q = \frac{c}{a}$$
$$q = -5.71482240437158$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1.51639344262295$$
$$x_{1} x_{2} = -5.71482240437158$$
Rapid solution
[src]
x1 = -3.26612109668228
$$x_{1} = -3.26612109668228$$
x2 = 1.74972765405933
$$x_{2} = 1.74972765405933$$
x2 = 1.74972765405933
Sum and product of roots
[src]
sum
-3.26612109668228 + 1.74972765405933
$$-3.26612109668228 + 1.74972765405933$$
=
-1.51639344262295
$$-1.51639344262295$$
product
-3.26612109668228*1.74972765405933
$$- 1.74972765405933 \cdot 3.26612109668228$$
=
-5.71482240437158
$$-5.71482240437158$$
-5.71482240437158