x^2+15x=2

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


Simplifying
x2 + 15x = 2

Reorder the terms:
15x + x2 = 2

Solving
15x + x2 = 2

Solving for variable 'x'.

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

Combine like terms: 2 + -2 = 0
-2 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 15x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 15x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 15x + x2 = 0 + 2
15x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
15x + x2 = 2

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 2 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 2 + 56.25

Combine like terms: 2 + 56.25 = 58.25
56.25 + 15x + x2 = 58.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 58.25

Calculate the square root of the right side: 7.632168761

Break this problem into two subproblems by setting 
(x + 7.5) equal to 7.632168761 and -7.632168761.

Subproblem 1

x + 7.5 = 7.632168761 Simplifying x + 7.5 = 7.632168761 Reorder the terms: 7.5 + x = 7.632168761 Solving 7.5 + x = 7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.632168761 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.632168761 + -7.5 x = 7.632168761 + -7.5 Combine like terms: 7.632168761 + -7.5 = 0.132168761 x = 0.132168761 Simplifying x = 0.132168761

Subproblem 2

x + 7.5 = -7.632168761 Simplifying x + 7.5 = -7.632168761 Reorder the terms: 7.5 + x = -7.632168761 Solving 7.5 + x = -7.632168761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.632168761 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.632168761 + -7.5 x = -7.632168761 + -7.5 Combine like terms: -7.632168761 + -7.5 = -15.132168761 x = -15.132168761 Simplifying x = -15.132168761

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.132168761, -15.132168761}

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