5x^2+13x=10

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Solution for 5x^2+13x=10 equation:


Simplifying
5x2 + 13x = 10

Reorder the terms:
13x + 5x2 = 10

Solving
13x + 5x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 13x + 5x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 13x + 5x2 = 0

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

Divide each side by '5'.
-2 + 2.6x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.6x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.6x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.6x + x2 = 0 + 2
2.6x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.6x + x2 = 2

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 2 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 2 + 1.69

Combine like terms: 2 + 1.69 = 3.69
1.69 + 2.6x + x2 = 3.69

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 3.69

Calculate the square root of the right side: 1.920937271

Break this problem into two subproblems by setting 
(x + 1.3) equal to 1.920937271 and -1.920937271.

Subproblem 1

x + 1.3 = 1.920937271 Simplifying x + 1.3 = 1.920937271 Reorder the terms: 1.3 + x = 1.920937271 Solving 1.3 + x = 1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 1.920937271 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 1.920937271 + -1.3 x = 1.920937271 + -1.3 Combine like terms: 1.920937271 + -1.3 = 0.620937271 x = 0.620937271 Simplifying x = 0.620937271

Subproblem 2

x + 1.3 = -1.920937271 Simplifying x + 1.3 = -1.920937271 Reorder the terms: 1.3 + x = -1.920937271 Solving 1.3 + x = -1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -1.920937271 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -1.920937271 + -1.3 x = -1.920937271 + -1.3 Combine like terms: -1.920937271 + -1.3 = -3.220937271 x = -3.220937271 Simplifying x = -3.220937271

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.620937271, -3.220937271}

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