0=4x^2-12x-35

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Solution for 0=4x^2-12x-35 equation:


Simplifying
0 = 4x2 + -12x + -35

Reorder the terms:
0 = -35 + -12x + 4x2

Solving
0 = -35 + -12x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 35 = 35
35 + 12x + -4x2 = -35 + -12x + 4x2 + 35 + 12x + -4x2

Reorder the terms:
35 + 12x + -4x2 = -35 + 35 + -12x + 12x + 4x2 + -4x2

Combine like terms: -35 + 35 = 0
35 + 12x + -4x2 = 0 + -12x + 12x + 4x2 + -4x2
35 + 12x + -4x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
35 + 12x + -4x2 = 0 + 4x2 + -4x2
35 + 12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
35 + 12x + -4x2 = 0

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

Divide each side by '-4'.
-8.75 + -3x + x2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + -3x + 8.75 + x2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + -3x + x2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + -3x + x2 = 0 + 8.75
-3x + x2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
-3x + x2 = 8.75

The x term is -3x.  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.
-3x + 2.25 + x2 = 8.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 8.75 + 2.25

Combine like terms: 8.75 + 2.25 = 11
2.25 + -3x + x2 = 11

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -1.5 = 3.31662479 Simplifying x + -1.5 = 3.31662479 Reorder the terms: -1.5 + x = 3.31662479 Solving -1.5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.31662479 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.31662479 + 1.5 x = 3.31662479 + 1.5 Combine like terms: 3.31662479 + 1.5 = 4.81662479 x = 4.81662479 Simplifying x = 4.81662479

Subproblem 2

x + -1.5 = -3.31662479 Simplifying x + -1.5 = -3.31662479 Reorder the terms: -1.5 + x = -3.31662479 Solving -1.5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.31662479 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.31662479 + 1.5 x = -3.31662479 + 1.5 Combine like terms: -3.31662479 + 1.5 = -1.81662479 x = -1.81662479 Simplifying x = -1.81662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.81662479, -1.81662479}

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