4x^2-16x=13

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Solution for 4x^2-16x=13 equation:


Simplifying
4x2 + -16x = 13

Reorder the terms:
-16x + 4x2 = 13

Solving
-16x + 4x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -16x + 4x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -16x + 4x2 = 0

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

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

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -4x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -4x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -4x + x2 = 0 + 3.25
-4x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-4x + x2 = 3.25

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 3.25 + 4

Reorder the terms:
4 + -4x + x2 = 3.25 + 4

Combine like terms: 3.25 + 4 = 7.25
4 + -4x + x2 = 7.25

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + -2) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + -2 = 2.692582404 Simplifying x + -2 = 2.692582404 Reorder the terms: -2 + x = 2.692582404 Solving -2 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.692582404 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.692582404 + 2 x = 2.692582404 + 2 Combine like terms: 2.692582404 + 2 = 4.692582404 x = 4.692582404 Simplifying x = 4.692582404

Subproblem 2

x + -2 = -2.692582404 Simplifying x + -2 = -2.692582404 Reorder the terms: -2 + x = -2.692582404 Solving -2 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.692582404 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.692582404 + 2 x = -2.692582404 + 2 Combine like terms: -2.692582404 + 2 = -0.692582404 x = -0.692582404 Simplifying x = -0.692582404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.692582404, -0.692582404}

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