4x^2+2x-105=0

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Solution for 4x^2+2x-105=0 equation:


Simplifying
4x2 + 2x + -105 = 0

Reorder the terms:
-105 + 2x + 4x2 = 0

Solving
-105 + 2x + 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'.
-26.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '26.25' to each side of the equation.
-26.25 + 0.5x + 26.25 + x2 = 0 + 26.25

Reorder the terms:
-26.25 + 26.25 + 0.5x + x2 = 0 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + 0.5x + x2 = 0 + 26.25
0.5x + x2 = 0 + 26.25

Combine like terms: 0 + 26.25 = 26.25
0.5x + x2 = 26.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 26.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 26.25 + 0.0625

Combine like terms: 26.25 + 0.0625 = 26.3125
0.0625 + 0.5x + x2 = 26.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 26.3125

Calculate the square root of the right side: 5.129571132

Break this problem into two subproblems by setting 
(x + 0.25) equal to 5.129571132 and -5.129571132.

Subproblem 1

x + 0.25 = 5.129571132 Simplifying x + 0.25 = 5.129571132 Reorder the terms: 0.25 + x = 5.129571132 Solving 0.25 + x = 5.129571132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 5.129571132 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 5.129571132 + -0.25 x = 5.129571132 + -0.25 Combine like terms: 5.129571132 + -0.25 = 4.879571132 x = 4.879571132 Simplifying x = 4.879571132

Subproblem 2

x + 0.25 = -5.129571132 Simplifying x + 0.25 = -5.129571132 Reorder the terms: 0.25 + x = -5.129571132 Solving 0.25 + x = -5.129571132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -5.129571132 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -5.129571132 + -0.25 x = -5.129571132 + -0.25 Combine like terms: -5.129571132 + -0.25 = -5.379571132 x = -5.379571132 Simplifying x = -5.379571132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.879571132, -5.379571132}

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