-4w^2+14w+9=0

Simple and best practice solution for -4w^2+14w+9=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 -4w^2+14w+9=0 equation:


Simplifying
-4w2 + 14w + 9 = 0

Reorder the terms:
9 + 14w + -4w2 = 0

Solving
9 + 14w + -4w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + -3.5w + w2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -3.5w + 2.25 + w2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -3.5w + w2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -3.5w + w2 = 0 + 2.25
-3.5w + w2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-3.5w + w2 = 2.25

The w term is -3.5w.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5w + 3.0625 + w2 = 2.25 + 3.0625

Reorder the terms:
3.0625 + -3.5w + w2 = 2.25 + 3.0625

Combine like terms: 2.25 + 3.0625 = 5.3125
3.0625 + -3.5w + w2 = 5.3125

Factor a perfect square on the left side:
(w + -1.75)(w + -1.75) = 5.3125

Calculate the square root of the right side: 2.304886114

Break this problem into two subproblems by setting 
(w + -1.75) equal to 2.304886114 and -2.304886114.

Subproblem 1

w + -1.75 = 2.304886114 Simplifying w + -1.75 = 2.304886114 Reorder the terms: -1.75 + w = 2.304886114 Solving -1.75 + w = 2.304886114 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = 2.304886114 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = 2.304886114 + 1.75 w = 2.304886114 + 1.75 Combine like terms: 2.304886114 + 1.75 = 4.054886114 w = 4.054886114 Simplifying w = 4.054886114

Subproblem 2

w + -1.75 = -2.304886114 Simplifying w + -1.75 = -2.304886114 Reorder the terms: -1.75 + w = -2.304886114 Solving -1.75 + w = -2.304886114 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + w = -2.304886114 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + w = -2.304886114 + 1.75 w = -2.304886114 + 1.75 Combine like terms: -2.304886114 + 1.75 = -0.554886114 w = -0.554886114 Simplifying w = -0.554886114

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.054886114, -0.554886114}

See similar equations:

| 1/4x^2-x-2=0 | | -5(X+1)-15=17+3 | | 8x+3y=62 | | -3p-6+2p=4p-9 | | 5y^2-16y+12=0 | | 5/p=-10 | | 6(9x-14)=240 | | 5x+28=3x | | 6/7=m/42 | | s^2+6s+6=0 | | 86=3/17*56+b | | 2x(3b+5a)= | | 8-d-15=-3d+15 | | 4a^2-b^2-2bc-c^2= | | (t-3)(2+3t)=0 | | 9y-7-8y=9-y | | -x^2-10x+10=0 | | (-4x-5)=26+-3x | | 6(x+4)-7= | | 6x-3=7x+7+4x | | (4x+5)=26-3x | | 8(-2x+6)-2=30 | | -2(5y-3)-y=-3(y-2) | | x+5/7=4 | | 10x+12.5= | | -7t+3t^2-6=0 | | (-7x+2)=x+4 | | (7x-2)=x+4 | | 1-4-16= | | (4x)=0 | | -5(t-2)+9t=8t-7 | | 50-7x=18+9x |

Equations solver categories