x^2+10x+15=18

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Solution for x^2+10x+15=18 equation:


Simplifying
x2 + 10x + 15 = 18

Reorder the terms:
15 + 10x + x2 = 18

Solving
15 + 10x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
15 + -18 + 10x + x2 = 18 + -18

Combine like terms: 15 + -18 = -3
-3 + 10x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-3 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 10x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 10x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 10x + x2 = 0 + 3
10x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
10x + x2 = 3

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 3 + 25

Reorder the terms:
25 + 10x + x2 = 3 + 25

Combine like terms: 3 + 25 = 28
25 + 10x + x2 = 28

Factor a perfect square on the left side:
(x + 5)(x + 5) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 5) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + 5 = 5.291502622 Simplifying x + 5 = 5.291502622 Reorder the terms: 5 + x = 5.291502622 Solving 5 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.291502622 + -5 x = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 x = 0.291502622 Simplifying x = 0.291502622

Subproblem 2

x + 5 = -5.291502622 Simplifying x + 5 = -5.291502622 Reorder the terms: 5 + x = -5.291502622 Solving 5 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.291502622 + -5 x = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 x = -10.291502622 Simplifying x = -10.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.291502622, -10.291502622}

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