x^2+x=17.5

Simple and best practice solution for x^2+x=17.5 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2+x=17.5 equation: 


Simplifying
x2 + x = 17.5

Reorder the terms:
x + x2 = 17.5

Solving
x + x2 = 17.5

Solving for variable 'x'.

Reorder the terms:
-17.5 + x + x2 = 17.5 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
-17.5 + x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + x + 17.5 + x2 = 0.0 + 17.5

Reorder the terms:
-17.5 + 17.5 + x + x2 = 0.0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x + x2 = 0.0 + 17.5
x + x2 = 0.0 + 17.5

Combine like terms: 0.0 + 17.5 = 17.5
x + x2 = 17.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 17.5 + 0.25

Reorder the terms:
0.25 + x + x2 = 17.5 + 0.25

Combine like terms: 17.5 + 0.25 = 17.75
0.25 + x + x2 = 17.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 17.75

Calculate the square root of the right side: 4.213074887

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.213074887 and -4.213074887.


Subproblem 1
x + 0.5 = 4.213074887

Simplifying
x + 0.5 = 4.213074887

Reorder the terms:
0.5 + x = 4.213074887

Solving
0.5 + x = 4.213074887

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.213074887 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.213074887 + -0.5
x = 4.213074887 + -0.5

Combine like terms: 4.213074887 + -0.5 = 3.713074887
x = 3.713074887

Simplifying
x = 3.713074887


Subproblem 2
x + 0.5 = -4.213074887

Simplifying
x + 0.5 = -4.213074887

Reorder the terms:
0.5 + x = -4.213074887

Solving
0.5 + x = -4.213074887

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.213074887 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.213074887 + -0.5
x = -4.213074887 + -0.5

Combine like terms: -4.213074887 + -0.5 = -4.713074887
x = -4.713074887

Simplifying
x = -4.713074887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.713074887, -4.713074887}

See similar equations:

| 10-3(4x-3)=2(3x-4)-9 | | 16m=14n | | 5/7*2/9 | | n=7-3 | | 70*.05+.10x=70+x | | 2/3(x-1)=11 | | x*(2*x-3)+x*(5*x-11)=0 | | (2w+3)/(-12)=1/4 | | 3/14=18/4w | | (6x+12)(11x+3)-(14x+13)(6x+12)=0 | | 4(t-6)+8t=4(3t+4)-9 | | 7.3=2X | | 11m^2+121= | | 3+d=8 | | y=0x-4 | | h=4+35x-16x^2 | | 2y+7x+9=0 | | 2X^3-Z= | | -11.5(9.5+6.4p)+1.9p(7.1p-5.552)= | | v=4/3+3.14+6^3 | | 12y^3+6y^2-36y=0 | | 12y+4x=360 | | 6(3-2x)-(1-x)=4(x-3) | | 6(-2n+12)+12(n-5)= | | (1/5)(6x+5)=8x | | 4x+2=4x^2 | | x-12x(5x+3)= | | 0.75x+0.5(4-x)=.10(.124) | | 10x^2+9x+20/5 | | 0.75x+0.5(4-x)= | | -4b(b+1)= | | Ln(5)+ln(x)=0 |

Equations solver categories