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x²+(x+2)²=10²

x²+(x+2)²=10² equation

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Numerical solution:

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The solution

You have entered [src] 
 2          2     2
x  + (x + 2)  = 10
x2+(x+2)2=102x^{2} + \left(x + 2\right)^{2} = 10^{2}
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2+(x+2)2=102x^{2} + \left(x + 2\right)^{2} = 10^{2}
to
(x2+(x+2)2)−102=0\left(x^{2} + \left(x + 2\right)^{2}\right) - 10^{2} = 0
Expand the expression in the equation
(x2+(x+2)2)−102=0\left(x^{2} + \left(x + 2\right)^{2}\right) - 10^{2} = 0
We get the quadratic equation
2x2+4x−100+4=02 x^{2} + 4 x - 100 + 4 = 0
This equation is of the form
a x2+b x+c=0a\ x^2 + b\ x + c = 0
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D=b2−4acD = b^2 - 4 a c is the discriminant.
Because
a=2a = 2
b=4b = 4
c=−96c = -96
, then
D=b2−4 a c=D = b^2 - 4\ a\ c =
42−2⋅4(−96)=7844^{2} - 2 \cdot 4 \left(-96\right) = 784
Because D > 0, then the equation has two roots.
x1=(−b+D)2ax_1 = \frac{(-b + \sqrt{D})}{2 a}
x2=(−b−D)2ax_2 = \frac{(-b - \sqrt{D})}{2 a}
or
x1=6x_{1} = 6
Simplify
x2=−8x_{2} = -8
Simplify
The graph
05-25-20-15-10-51015200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-8 + 6
(−8)+(6)\left(-8\right) + \left(6\right) 
=
-2
−2-2
Simplify 
product
-8 * 6
(−8)∗(6)\left(-8\right) * \left(6\right) 
=
-48
−48-48
Simplify
Rapid solution [src] 
x_1 = -8
x1=−8x_{1} = -8
Simplify 
x_2 = 6
x2=6x_{2} = 6
Simplify
Numerical answer [src] 
x1 = -8.0
x2 = 6.0
x2 = 6.0
The graph
x²+(x+2)²=10² equation
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