4x^2-45x-126=0

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Solution for 4x^2-45x-126=0 equation:


Simplifying
4x2 + -45x + -126 = 0

Reorder the terms:
-126 + -45x + 4x2 = 0

Solving
-126 + -45x + 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'.
-31.5 + -11.25x + x2 = 0

Move the constant term to the right:

Add '31.5' to each side of the equation.
-31.5 + -11.25x + 31.5 + x2 = 0 + 31.5

Reorder the terms:
-31.5 + 31.5 + -11.25x + x2 = 0 + 31.5

Combine like terms: -31.5 + 31.5 = 0.0
0.0 + -11.25x + x2 = 0 + 31.5
-11.25x + x2 = 0 + 31.5

Combine like terms: 0 + 31.5 = 31.5
-11.25x + x2 = 31.5

The x term is -11.25x.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25x + 31.640625 + x2 = 31.5 + 31.640625

Reorder the terms:
31.640625 + -11.25x + x2 = 31.5 + 31.640625

Combine like terms: 31.5 + 31.640625 = 63.140625
31.640625 + -11.25x + x2 = 63.140625

Factor a perfect square on the left side:
(x + -5.625)(x + -5.625) = 63.140625

Calculate the square root of the right side: 7.946107538

Break this problem into two subproblems by setting 
(x + -5.625) equal to 7.946107538 and -7.946107538.

Subproblem 1

x + -5.625 = 7.946107538 Simplifying x + -5.625 = 7.946107538 Reorder the terms: -5.625 + x = 7.946107538 Solving -5.625 + x = 7.946107538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 7.946107538 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 7.946107538 + 5.625 x = 7.946107538 + 5.625 Combine like terms: 7.946107538 + 5.625 = 13.571107538 x = 13.571107538 Simplifying x = 13.571107538

Subproblem 2

x + -5.625 = -7.946107538 Simplifying x + -5.625 = -7.946107538 Reorder the terms: -5.625 + x = -7.946107538 Solving -5.625 + x = -7.946107538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -7.946107538 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -7.946107538 + 5.625 x = -7.946107538 + 5.625 Combine like terms: -7.946107538 + 5.625 = -2.321107538 x = -2.321107538 Simplifying x = -2.321107538

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.571107538, -2.321107538}

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