4x^2+5x-55=0

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Solution for 4x^2+5x-55=0 equation:


Simplifying
4x2 + 5x + -55 = 0

Reorder the terms:
-55 + 5x + 4x2 = 0

Solving
-55 + 5x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-13.75 + 1.25x + x2 = 0

Move the constant term to the right:

Add '13.75' to each side of the equation.
-13.75 + 1.25x + 13.75 + x2 = 0 + 13.75

Reorder the terms:
-13.75 + 13.75 + 1.25x + x2 = 0 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + 1.25x + x2 = 0 + 13.75
1.25x + x2 = 0 + 13.75

Combine like terms: 0 + 13.75 = 13.75
1.25x + x2 = 13.75

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 13.75 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 13.75 + 0.390625

Combine like terms: 13.75 + 0.390625 = 14.140625
0.390625 + 1.25x + x2 = 14.140625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 14.140625

Calculate the square root of the right side: 3.760402239

Break this problem into two subproblems by setting 
(x + 0.625) equal to 3.760402239 and -3.760402239.

Subproblem 1

x + 0.625 = 3.760402239 Simplifying x + 0.625 = 3.760402239 Reorder the terms: 0.625 + x = 3.760402239 Solving 0.625 + x = 3.760402239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.760402239 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.760402239 + -0.625 x = 3.760402239 + -0.625 Combine like terms: 3.760402239 + -0.625 = 3.135402239 x = 3.135402239 Simplifying x = 3.135402239

Subproblem 2

x + 0.625 = -3.760402239 Simplifying x + 0.625 = -3.760402239 Reorder the terms: 0.625 + x = -3.760402239 Solving 0.625 + x = -3.760402239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.760402239 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.760402239 + -0.625 x = -3.760402239 + -0.625 Combine like terms: -3.760402239 + -0.625 = -4.385402239 x = -4.385402239 Simplifying x = -4.385402239

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.135402239, -4.385402239}

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