Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4=(x-56)^2
-
Equation 16x-3=8x-43
- Equation x^2-x-72=0
-
Equation 15/6*x-1=x+2
- Express {x} in terms of y where:
- -7*x-13*y=-12
- 8*x+1*y=4
- 20*x-16*y=7
- -3*x+19*y=16
-
Identical expressions
- (x- nineteen)*(x+ four)= zero
- (x minus 19) multiply by (x plus 4) equally 0
- (x minus nineteen) multiply by (x plus four) equally zero
- (x-19)(x+4)=0
- x-19x+4=0
- (x-19)*(x+4)=O
-
Similar expressions
- (x+19)*(x+4)=0
- (x-19)*(x-4)=0
(x-19)*(x+4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 19\right) \left(x + 4\right) = 0$$
We get the quadratic equation
$$x^{2} - 15 x - 76 = 0$$
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
$$a = 1$$
$$b = -15$$
$$c = -76$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 19$$
$$x_{2} = -4$$
$$\left(x - 19\right) \left(x + 4\right) = 0$$
We get the quadratic equation
$$x^{2} - 15 x - 76 = 0$$
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
$$a = 1$$
$$b = -15$$
$$c = -76$$
, then
D = b^2 - 4 * a * c =
(-15)^2 - 4 * (1) * (-76) = 529
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 19$$
$$x_{2} = -4$$
Sum and product of roots
[src]
sum
-4 + 19
$$-4 + 19$$
=
15
$$15$$
product
-4*19
$$- 76$$
=
-76
$$-76$$
-76