### Other calculators # x^2=7 equation

A equation with variable:

#### Numerical solution:

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### The solution

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x  = 7
$$x^{2} = 7$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$x^{2} = 7$$
to
$$x^{2} - 7 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =

(0)^2 - 4 * (1) * (-7) = 28

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

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

or
$$x_{1} = \sqrt{7}$$
$$x_{2} = - \sqrt{7}$$
The graph
Rapid solution [src]
        ___
x1 = -\/ 7 
$$x_{1} = - \sqrt{7}$$
       ___
x2 = \/ 7 
$$x_{2} = \sqrt{7}$$
x2 = sqrt(7)
Sum and product of roots [src]
sum
    ___     ___
- \/ 7  + \/ 7 
$$- \sqrt{7} + \sqrt{7}$$
=
0
$$0$$
product
   ___   ___
-\/ 7 *\/ 7 
$$- \sqrt{7} \sqrt{7}$$
=
-7
$$-7$$
-7
Vieta's Theorem
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -7$$
x1 = -2.64575131106459
x2 = 2.64575131106459
x2 = 2.64575131106459