2x^2+13x+15=2

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Solution for 2x^2+13x+15=2 equation:


Simplifying
2x2 + 13x + 15 = 2

Reorder the terms:
15 + 13x + 2x2 = 2

Solving
15 + 13x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
15 + -2 + 13x + 2x2 = 2 + -2

Combine like terms: 15 + -2 = 13
13 + 13x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
13 + 13x + 2x2 = 0

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

Divide each side by '2'.
6.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 6.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 6.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 6.5x + x2 = 0 + -6.5
6.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
6.5x + x2 = -6.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -6.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -6.5 + 10.5625

Combine like terms: -6.5 + 10.5625 = 4.0625
10.5625 + 6.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 3.25) equal to 2.015564437 and -2.015564437.

Subproblem 1

x + 3.25 = 2.015564437 Simplifying x + 3.25 = 2.015564437 Reorder the terms: 3.25 + x = 2.015564437 Solving 3.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 2.015564437 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 2.015564437 + -3.25 x = 2.015564437 + -3.25 Combine like terms: 2.015564437 + -3.25 = -1.234435563 x = -1.234435563 Simplifying x = -1.234435563

Subproblem 2

x + 3.25 = -2.015564437 Simplifying x + 3.25 = -2.015564437 Reorder the terms: 3.25 + x = -2.015564437 Solving 3.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -2.015564437 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -2.015564437 + -3.25 x = -2.015564437 + -3.25 Combine like terms: -2.015564437 + -3.25 = -5.265564437 x = -5.265564437 Simplifying x = -5.265564437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.234435563, -5.265564437}

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