x^2+6x+10=15

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Solution for x^2+6x+10=15 equation:


Simplifying
x2 + 6x + 10 = 15

Reorder the terms:
10 + 6x + x2 = 15

Solving
10 + 6x + x2 = 15

Solving for variable 'x'.

Reorder the terms:
10 + -15 + 6x + x2 = 15 + -15

Combine like terms: 10 + -15 = -5
-5 + 6x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-5 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 6x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6x + x2 = 0 + 5
6x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
6x + x2 = 5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 5 + 9

Reorder the terms:
9 + 6x + x2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6x + x2 = 14

Factor a perfect square on the left side:
(x + 3)(x + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + 3 = 3.741657387 Simplifying x + 3 = 3.741657387 Reorder the terms: 3 + x = 3.741657387 Solving 3 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.741657387 + -3 x = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 x = 0.741657387 Simplifying x = 0.741657387

Subproblem 2

x + 3 = -3.741657387 Simplifying x + 3 = -3.741657387 Reorder the terms: 3 + x = -3.741657387 Solving 3 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.741657387 + -3 x = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 x = -6.741657387 Simplifying x = -6.741657387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.741657387, -6.741657387}

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