4x^2-13x=3

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Solution for 4x^2-13x=3 equation:


Simplifying
4x2 + -13x = 3

Reorder the terms:
-13x + 4x2 = 3

Solving
-13x + 4x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -13x + 4x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -13x + 4x2 = 0

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

Divide each side by '4'.
-0.75 + -3.25x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -3.25x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -3.25x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -3.25x + x2 = 0 + 0.75
-3.25x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-3.25x + x2 = 0.75

The x term is -3.25x.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25x + 2.640625 + x2 = 0.75 + 2.640625

Reorder the terms:
2.640625 + -3.25x + x2 = 0.75 + 2.640625

Combine like terms: 0.75 + 2.640625 = 3.390625
2.640625 + -3.25x + x2 = 3.390625

Factor a perfect square on the left side:
(x + -1.625)(x + -1.625) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(x + -1.625) equal to 1.841364983 and -1.841364983.

Subproblem 1

x + -1.625 = 1.841364983 Simplifying x + -1.625 = 1.841364983 Reorder the terms: -1.625 + x = 1.841364983 Solving -1.625 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.841364983 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.841364983 + 1.625 x = 1.841364983 + 1.625 Combine like terms: 1.841364983 + 1.625 = 3.466364983 x = 3.466364983 Simplifying x = 3.466364983

Subproblem 2

x + -1.625 = -1.841364983 Simplifying x + -1.625 = -1.841364983 Reorder the terms: -1.625 + x = -1.841364983 Solving -1.625 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.841364983 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.841364983 + 1.625 x = -1.841364983 + 1.625 Combine like terms: -1.841364983 + 1.625 = -0.216364983 x = -0.216364983 Simplifying x = -0.216364983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.466364983, -0.216364983}

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