w^2+3w-11=0

Simple and best practice solution for w^2+3w-11=0 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 w^2+3w-11=0 equation:


Simplifying
w2 + 3w + -11 = 0

Reorder the terms:
-11 + 3w + w2 = 0

Solving
-11 + 3w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 3w + 11 + w2 = 0 + 11

Reorder the terms:
-11 + 11 + 3w + w2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 3w + w2 = 0 + 11
3w + w2 = 0 + 11

Combine like terms: 0 + 11 = 11
3w + w2 = 11

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 11 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 11 + 2.25

Combine like terms: 11 + 2.25 = 13.25
2.25 + 3w + w2 = 13.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(w + 1.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

w + 1.5 = 3.640054945 Simplifying w + 1.5 = 3.640054945 Reorder the terms: 1.5 + w = 3.640054945 Solving 1.5 + w = 3.640054945 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 3.640054945 + -1.5 w = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 w = 2.140054945 Simplifying w = 2.140054945

Subproblem 2

w + 1.5 = -3.640054945 Simplifying w + 1.5 = -3.640054945 Reorder the terms: 1.5 + w = -3.640054945 Solving 1.5 + w = -3.640054945 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -3.640054945 + -1.5 w = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 w = -5.140054945 Simplifying w = -5.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.140054945, -5.140054945}

See similar equations:

| 34/5x21/9 | | 3x-8+7x+4/2=33 | | 4(2-1.5y)-6y=8 | | 4b-4=3b-2 | | 2x-8y=56 | | 5x+1=9x+6 | | -3x+4=-10 | | 5x+6=x+30 | | 6x-17=13x-13-4 | | 6x-16x^2=1.5 | | 5y+4y(y-7)=4(y+2)-4 | | (X-7/5)=1/2 | | -0.8x(x-8)=0.4x+3.2 | | A=3h | | 9(2n+4)=6(6n+7)+5 | | 5+2y-x=0 | | -5=3+c/5 | | -15w/-12 | | 16x^2-6x+1.5=0 | | 3+5f=(-32) | | 4(2n+3)=7(6n+2)+7 | | 800/20/4 | | Tanx=1.33333 | | 16=x+2+3x-10 | | 0.7x-2.7=0.8 | | 4h+9=113 | | 8x=74 | | (7/3)-(x/3)=x/4 | | 9(x-1)/3=6(x+3)/10 | | 16=.5xy+2+3y-10 | | 90+24=126+30 | | -5/12+1/3 |

Equations solver categories