4x^2+13x-0.5=0

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Solution for 4x^2+13x-0.5=0 equation:


Simplifying
4x2 + 13x + -0.5 = 0

Reorder the terms:
-0.5 + 13x + 4x2 = 0

Solving
-0.5 + 13x + 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'.
-0.125 + 3.25x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 3.25x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 3.25x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 3.25x + x2 = 0 + 0.125
3.25x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
3.25x + x2 = 0.125

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 = 0.125 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 0.125 + 2.640625

Combine like terms: 0.125 + 2.640625 = 2.765625
2.640625 + 3.25x + x2 = 2.765625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 2.765625

Calculate the square root of the right side: 1.663016837

Break this problem into two subproblems by setting 
(x + 1.625) equal to 1.663016837 and -1.663016837.

Subproblem 1

x + 1.625 = 1.663016837 Simplifying x + 1.625 = 1.663016837 Reorder the terms: 1.625 + x = 1.663016837 Solving 1.625 + x = 1.663016837 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 = 1.663016837 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.663016837 + -1.625 x = 1.663016837 + -1.625 Combine like terms: 1.663016837 + -1.625 = 0.038016837 x = 0.038016837 Simplifying x = 0.038016837

Subproblem 2

x + 1.625 = -1.663016837 Simplifying x + 1.625 = -1.663016837 Reorder the terms: 1.625 + x = -1.663016837 Solving 1.625 + x = -1.663016837 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 = -1.663016837 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.663016837 + -1.625 x = -1.663016837 + -1.625 Combine like terms: -1.663016837 + -1.625 = -3.288016837 x = -3.288016837 Simplifying x = -3.288016837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.038016837, -3.288016837}

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