2x^2+3x=220

Simple and best practice solution for 2x^2+3x=220 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 2x^2+3x=220 equation:


Simplifying
2x2 + 3x = 220

Reorder the terms:
3x + 2x2 = 220

Solving
3x + 2x2 = 220

Solving for variable 'x'.

Reorder the terms:
-220 + 3x + 2x2 = 220 + -220

Combine like terms: 220 + -220 = 0
-220 + 3x + 2x2 = 0

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

Divide each side by '2'.
-110 + 1.5x + x2 = 0

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 1.5x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + 1.5x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 1.5x + x2 = 0 + 110
1.5x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
1.5x + x2 = 110

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 110 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 110 + 0.5625

Combine like terms: 110 + 0.5625 = 110.5625
0.5625 + 1.5x + x2 = 110.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 110.5625

Calculate the square root of the right side: 10.514870422

Break this problem into two subproblems by setting 
(x + 0.75) equal to 10.514870422 and -10.514870422.

Subproblem 1

x + 0.75 = 10.514870422 Simplifying x + 0.75 = 10.514870422 Reorder the terms: 0.75 + x = 10.514870422 Solving 0.75 + x = 10.514870422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 10.514870422 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 10.514870422 + -0.75 x = 10.514870422 + -0.75 Combine like terms: 10.514870422 + -0.75 = 9.764870422 x = 9.764870422 Simplifying x = 9.764870422

Subproblem 2

x + 0.75 = -10.514870422 Simplifying x + 0.75 = -10.514870422 Reorder the terms: 0.75 + x = -10.514870422 Solving 0.75 + x = -10.514870422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -10.514870422 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -10.514870422 + -0.75 x = -10.514870422 + -0.75 Combine like terms: -10.514870422 + -0.75 = -11.264870422 x = -11.264870422 Simplifying x = -11.264870422

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.764870422, -11.264870422}

See similar equations:

| 12y^2+12y=144 | | 54=14-8a | | 4(x-6)+3=7 | | 2z^2+3z-7=0 | | 5p(-5)=105 | | Y=(x-2)2 | | x+x+9+x+x+9=301 | | 505p(-5)=1 | | -5x+6x=4-5(2x+1) | | 4(6c+1)-22=20c+2 | | 1024+1225-2*32*35Cos(x)=484 | | 4x-9=-3x+6 | | 1/7(x-2)=-16-2 | | 13y-7y=9 | | 7x-8=2x+20 | | 20.6+2.1y=-8.2y | | s*4-26=78 | | 21=7+4x | | 2t/16 | | (2x+10)=(x-20) | | x-2+x-2+x-2=143 | | p^2+28+11x=0 | | x^3-3x^2+3x-2=0 | | 0.15(x+2000)=8x+20 | | sinx=0.092 | | 3y-y-20=8 | | 2(x+4)=5x+7 | | 6x+3x-5=4x+8+3x | | x+3x+x+3x=100 | | 22p^2+34p-36=0 | | 4v+9=77 | | 20=18x |

Equations solver categories