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x^2+3x-28=0

x^2+3x-28=0 equation

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Numerical solution:

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The solution

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 2               
x  + 3*x - 28 = 0
x2+3x−28=0x^{2} + 3 x - 28 = 0
Simplify
Detail solution
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=1a = 1
b=3b = 3
c=−28c = -28
, then
D=b2−4 a c=D = b^2 - 4\ a\ c =
32−1⋅4(−28)=1213^{2} - 1 \cdot 4 \left(-28\right) = 121
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=4x_{1} = 4
Simplify
x2=−7x_{2} = -7
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=3p = 3
q=caq = \frac{c}{a}
q=−28q = -28
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−3x_{1} + x_{2} = -3
x1x2=−28x_{1} x_{2} = -28
The graph
-7.5-5.0-2.50.02.55.07.510.012.515.017.520.0-100100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x_1 = -7
x1=−7x_{1} = -7
Simplify 
x_2 = 4
x2=4x_{2} = 4
Simplify
Sum and product of roots [src] 
sum
-7 + 4
(−7)+(4)\left(-7\right) + \left(4\right) 
=
-3
−3-3
Simplify 
product
-7 * 4
(−7)∗(4)\left(-7\right) * \left(4\right) 
=
-28
−28-28
Simplify
Numerical answer [src] 
x1 = 4.0
x2 = -7.0
x2 = -7.0
The graph
x^2+3x-28=0 equation
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