Mister Exam
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Identical expressions
- (x- ten)²- eighty-one = zero
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- x-10²-81=0
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Similar expressions
- (x+10)²-81=0
- (x-10)²+81=0
(x-10)²-81=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 10\right)^{2} - 81 = 0$$
We get the quadratic equation
$$x^{2} - 20 x + 19 = 0$$
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
$$a = 1$$
$$b = -20$$
$$c = 19$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 19$$
$$x_{2} = 1$$
$$\left(x - 10\right)^{2} - 81 = 0$$
We get the quadratic equation
$$x^{2} - 20 x + 19 = 0$$
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
$$a = 1$$
$$b = -20$$
$$c = 19$$
, then
D = b^2 - 4 * a * c =
(-20)^2 - 4 * (1) * (19) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 19$$
$$x_{2} = 1$$