Mister Exam

Other calculators

5x-25+2x²=17+13x​

5x-25+2x²=17+13x​ equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
              2            
5*x - 25 + 2*x  = 17 + 13*x
2x2+5x−25=13x+172 x^{2} + 5 x - 25 = 13 x + 17
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
2x2+5x−25=13x+172 x^{2} + 5 x - 25 = 13 x + 17
to
(−13x−17)+(2x2+5x−25)=0\left(- 13 x - 17\right) + \left(2 x^{2} + 5 x - 25\right) = 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=−8b = -8
c=−42c = -42
, then
D=b2−4 a c=D = b^2 - 4\ a\ c =
(−8)2−2⋅4(−42)=400\left(-8\right)^{2} - 2 \cdot 4 \left(-42\right) = 400
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=7x_{1} = 7
Simplify
x2=−3x_{2} = -3
Simplify
Vieta's Theorem
rewrite the equation
2x2+5x−25=13x+172 x^{2} + 5 x - 25 = 13 x + 17
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−4x−21=0x^{2} - 4 x - 21 = 0
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=−4p = -4
q=caq = \frac{c}{a}
q=−21q = -21
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=4x_{1} + x_{2} = 4
x1x2=−21x_{1} x_{2} = -21
The graph
-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.515.0-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x_1 = -3
x1=−3x_{1} = -3
Simplify 
x_2 = 7
x2=7x_{2} = 7
Simplify
Sum and product of roots [src] 
sum
-3 + 7
(−3)+(7)\left(-3\right) + \left(7\right) 
=
4
44
Simplify 
product
-3 * 7
(−3)∗(7)\left(-3\right) * \left(7\right) 
=
-21
−21-21
Simplify
Numerical answer [src] 
x1 = 7.0
x2 = -3.0
x2 = -3.0
The graph
5x-25+2x²=17+13x​ equation
    © Mister Exam – Calculator