4x^2+30x-105=0

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Solution for 4x^2+30x-105=0 equation:


Simplifying
4x2 + 30x + -105 = 0

Reorder the terms:
-105 + 30x + 4x2 = 0

Solving
-105 + 30x + 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 + 7.5x + x2 = 0

Move the constant term to the right:

Add '26.25' to each side of the equation.
-26.25 + 7.5x + 26.25 + x2 = 0 + 26.25

Reorder the terms:
-26.25 + 26.25 + 7.5x + x2 = 0 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + 7.5x + x2 = 0 + 26.25
7.5x + x2 = 0 + 26.25

Combine like terms: 0 + 26.25 = 26.25
7.5x + x2 = 26.25

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 26.25 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 26.25 + 14.0625

Combine like terms: 26.25 + 14.0625 = 40.3125
14.0625 + 7.5x + x2 = 40.3125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 40.3125

Calculate the square root of the right side: 6.34921255

Break this problem into two subproblems by setting 
(x + 3.75) equal to 6.34921255 and -6.34921255.

Subproblem 1

x + 3.75 = 6.34921255 Simplifying x + 3.75 = 6.34921255 Reorder the terms: 3.75 + x = 6.34921255 Solving 3.75 + x = 6.34921255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 6.34921255 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 6.34921255 + -3.75 x = 6.34921255 + -3.75 Combine like terms: 6.34921255 + -3.75 = 2.59921255 x = 2.59921255 Simplifying x = 2.59921255

Subproblem 2

x + 3.75 = -6.34921255 Simplifying x + 3.75 = -6.34921255 Reorder the terms: 3.75 + x = -6.34921255 Solving 3.75 + x = -6.34921255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -6.34921255 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -6.34921255 + -3.75 x = -6.34921255 + -3.75 Combine like terms: -6.34921255 + -3.75 = -10.09921255 x = -10.09921255 Simplifying x = -10.09921255

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.59921255, -10.09921255}

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