Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x-2+3*(x-3)=3*(4-x)-3
-
Equation 3*x+50=77
-
Equation x^2+2x-24=0
- Equation (x-7)(-5x-9)=0
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 18*x-12*y=-20
- -11*x+6*y=4
- 14*x-13*y=-10
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Identical expressions
- (x- seven)(-5x- nine)= zero
- (x minus 7)( minus 5x minus 9) equally 0
- (x minus seven)( minus 5x minus nine) equally zero
- x-7-5x-9=0
- (x-7)(-5x-9)=O
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Similar expressions
- (x-7)(5x-9)=0
- (x-7)(-5x+9)=0
- (x+7)(-5x-9)=0
(x-7)(-5x-9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- 5 x - 9\right) \left(x - 7\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 26 x + 63 = 0$$
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
$$a = -5$$
$$b = 26$$
$$c = 63$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{9}{5}$$
$$x_{2} = 7$$
$$\left(- 5 x - 9\right) \left(x - 7\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 26 x + 63 = 0$$
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
$$a = -5$$
$$b = 26$$
$$c = 63$$
, then
D = b^2 - 4 * a * c =
(26)^2 - 4 * (-5) * (63) = 1936
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{9}{5}$$
$$x_{2} = 7$$
Sum and product of roots
[src]
sum
7 - 9/5
$$- \frac{9}{5} + 7$$
=
26/5
$$\frac{26}{5}$$
product
7*(-9) ------ 5
$$\frac{\left(-9\right) 7}{5}$$
=
-63/5
$$- \frac{63}{5}$$
-63/5