10x^2+5x=18

Simple and best practice solution for 10x^2+5x=18 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 10x^2+5x=18 equation:


Simplifying
10x2 + 5x = 18

Reorder the terms:
5x + 10x2 = 18

Solving
5x + 10x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 5x + 10x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 5x + 10x2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
-1.8 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 0.5x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 0.5x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 0.5x + x2 = 0 + 1.8
0.5x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
0.5x + x2 = 1.8

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.8 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.8 + 0.0625

Combine like terms: 1.8 + 0.0625 = 1.8625
0.0625 + 0.5x + x2 = 1.8625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.8625

Calculate the square root of the right side: 1.364734406

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.364734406 and -1.364734406.

Subproblem 1

x + 0.25 = 1.364734406 Simplifying x + 0.25 = 1.364734406 Reorder the terms: 0.25 + x = 1.364734406 Solving 0.25 + x = 1.364734406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.364734406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.364734406 + -0.25 x = 1.364734406 + -0.25 Combine like terms: 1.364734406 + -0.25 = 1.114734406 x = 1.114734406 Simplifying x = 1.114734406

Subproblem 2

x + 0.25 = -1.364734406 Simplifying x + 0.25 = -1.364734406 Reorder the terms: 0.25 + x = -1.364734406 Solving 0.25 + x = -1.364734406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.364734406 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.364734406 + -0.25 x = -1.364734406 + -0.25 Combine like terms: -1.364734406 + -0.25 = -1.614734406 x = -1.614734406 Simplifying x = -1.614734406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.114734406, -1.614734406}

See similar equations:

| -2y+(-y)=18 | | 2x-9y=30 | | 3(n-45.86)=60.54 | | 4/5x-4/5=7 | | y=2x^2+12x+28 | | 5r+7=3r-15 | | 7w-6w+1=13 | | -9n-(-10n)=-5 | | 9x=7(x+10) | | 2.48x+9.92=19.84 | | 10y-3(y+5)= | | -18u+12u=6 | | k-705/16=11 | | 40-8n=-4(8+8n) | | 8x-2(2x+1)=3x-10 | | 16q-14q+4=12 | | t-67/3=6 | | -8x-9=2x+15 | | f(t)=-t^2+3t+4 | | 4x-2x+1=5 | | 3823734l+83474746= | | 7y+7y=-12 | | 5x+5=17-3x | | 0129837465+-109283659326= | | 22/55=12/h= | | 18x-15x-1=14 | | 2b-11=-4+2b+13 | | 3x-43=48 | | 2/3x-4/3=4 | | 4(d+2)=10 | | x/3?7x/9=3 | | 5j+j+2=8 |

Equations solver categories