w^2+3w-114=0

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Solution for w^2+3w-114=0 equation:


Simplifying
w2 + 3w + -114 = 0

Reorder the terms:
-114 + 3w + w2 = 0

Solving
-114 + 3w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + 3w + 114 + w2 = 0 + 114

Reorder the terms:
-114 + 114 + 3w + w2 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + 3w + w2 = 0 + 114
3w + w2 = 0 + 114

Combine like terms: 0 + 114 = 114
3w + w2 = 114

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 = 114 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 114 + 2.25

Combine like terms: 114 + 2.25 = 116.25
2.25 + 3w + w2 = 116.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 116.25

Calculate the square root of the right side: 10.781929326

Break this problem into two subproblems by setting 
(w + 1.5) equal to 10.781929326 and -10.781929326.

Subproblem 1

w + 1.5 = 10.781929326 Simplifying w + 1.5 = 10.781929326 Reorder the terms: 1.5 + w = 10.781929326 Solving 1.5 + w = 10.781929326 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 = 10.781929326 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 10.781929326 + -1.5 w = 10.781929326 + -1.5 Combine like terms: 10.781929326 + -1.5 = 9.281929326 w = 9.281929326 Simplifying w = 9.281929326

Subproblem 2

w + 1.5 = -10.781929326 Simplifying w + 1.5 = -10.781929326 Reorder the terms: 1.5 + w = -10.781929326 Solving 1.5 + w = -10.781929326 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 = -10.781929326 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -10.781929326 + -1.5 w = -10.781929326 + -1.5 Combine like terms: -10.781929326 + -1.5 = -12.281929326 w = -12.281929326 Simplifying w = -12.281929326

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.281929326, -12.281929326}

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