4x^2+13x-10=0

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Solution for 4x^2+13x-10=0 equation:


Simplifying
4x2 + 13x + -10 = 0

Reorder the terms:
-10 + 13x + 4x2 = 0

Solving
-10 + 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'.
-2.5 + 3.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 3.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 3.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 3.25x + x2 = 0 + 2.5
3.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
3.25x + x2 = 2.5

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 = 2.5 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 2.5 + 2.640625

Combine like terms: 2.5 + 2.640625 = 5.140625
2.640625 + 3.25x + x2 = 5.140625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 5.140625

Calculate the square root of the right side: 2.267294643

Break this problem into two subproblems by setting 
(x + 1.625) equal to 2.267294643 and -2.267294643.


Subproblem 1
x + 1.625 = 2.267294643

Simplifying
x + 1.625 = 2.267294643

Reorder the terms:
1.625 + x = 2.267294643

Solving
1.625 + x = 2.267294643

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 = 2.267294643 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = 2.267294643 + -1.625
x = 2.267294643 + -1.625

Combine like terms: 2.267294643 + -1.625 = 0.642294643
x = 0.642294643

Simplifying
x = 0.642294643


Subproblem 2
x + 1.625 = -2.267294643

Simplifying
x + 1.625 = -2.267294643

Reorder the terms:
1.625 + x = -2.267294643

Solving
1.625 + x = -2.267294643

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 = -2.267294643 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = -2.267294643 + -1.625
x = -2.267294643 + -1.625

Combine like terms: -2.267294643 + -1.625 = -3.892294643
x = -3.892294643

Simplifying
x = -3.892294643


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.642294643, -3.892294643}

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