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12-x^2=11

12-x^2=11 equation

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Numerical solution:

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The solution

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12 - x  = 11
$$12 - x^{2} = 11$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$12 - x^{2} = 11$$
to
$$\left(12 - x^{2}\right) - 11 = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 1$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (-1) * (1) = 4

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = -1$$
$$x_{2} = 1$$
Vieta's Theorem
rewrite the equation
$$12 - x^{2} = 11$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
The graph
Rapid solution [src]
x1 = -1
$$x_{1} = -1$$
x2 = 1
$$x_{2} = 1$$
x2 = 1
Sum and product of roots [src]
sum
-1 + 1
$$-1 + 1$$
=
0
$$0$$
product
-1
$$-1$$
=
-1
$$-1$$
-1
Numerical answer [src]
x1 = 1.0
x2 = -1.0
x2 = -1.0
The graph
12-x^2=11 equation