2x^2-11x=16

Simple and best practice solution for 2x^2-11x=16 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^2-11x=16 equation:


Simplifying
2x2 + -11x = 16

Reorder the terms:
-11x + 2x2 = 16

Solving
-11x + 2x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -11x + 2x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -11x + 2x2 = 0

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

Divide each side by '2'.
-8 + -5.5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -5.5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -5.5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5.5x + x2 = 0 + 8
-5.5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5.5x + x2 = 8

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 8 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 8 + 7.5625

Combine like terms: 8 + 7.5625 = 15.5625
7.5625 + -5.5x + x2 = 15.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 15.5625

Calculate the square root of the right side: 3.94493346

Break this problem into two subproblems by setting 
(x + -2.75) equal to 3.94493346 and -3.94493346.

Subproblem 1

x + -2.75 = 3.94493346 Simplifying x + -2.75 = 3.94493346 Reorder the terms: -2.75 + x = 3.94493346 Solving -2.75 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.94493346 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.94493346 + 2.75 x = 3.94493346 + 2.75 Combine like terms: 3.94493346 + 2.75 = 6.69493346 x = 6.69493346 Simplifying x = 6.69493346

Subproblem 2

x + -2.75 = -3.94493346 Simplifying x + -2.75 = -3.94493346 Reorder the terms: -2.75 + x = -3.94493346 Solving -2.75 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.94493346 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.94493346 + 2.75 x = -3.94493346 + 2.75 Combine like terms: -3.94493346 + 2.75 = -1.19493346 x = -1.19493346 Simplifying x = -1.19493346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.69493346, -1.19493346}

See similar equations:

| 4x^2+13x=10 | | 3x+10+x=18 | | 9x+20=4x-25 | | 7y+7=14y+7 | | y=x^2-5x+6 | | -6x+12=40-2x | | 2(3x+11)=5(x+7) | | 5x+12=-103 | | 3(6x+4)=58 | | 5(9+6x)=105 | | -7y=42 | | 3x+6=8+x | | 2x-15=8x-3 | | 7(8+x)=28 | | -5x+9-x=-45 | | 5(7+7x)=-105 | | -5(-5+6x)=-305 | | 25x^2-20x-3=0 | | r^3-64=0 | | -5(-10+4x)=10 | | 8+3x+2x=43 | | 3(-4x+4)=84 | | 3x+8=5x+18 | | 14x-13=8x-7 | | 7x-4=4x+17 | | -2x+10=-38+4x | | 6+3x=-2x-39 | | 3x+6=7x+2 | | (x+6)1.5=2x | | 3x+1=10-6x | | 10k-4k=12 | | 9+2x=-3x-51 |

Equations solver categories