21+(x+3)x=180

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Solution for 21+(x+3)x=180 equation:


Simplifying
21 + (x + 3) * x = 180
Reorder the terms:
21 + (3 + x) * x = 180
Reorder the terms for easier multiplication:
21 + x(3 + x) = 180
21 + (3 * x + x * x) = 180
21 + (3x + x2) = 180
Solving
21 + 3x + x2 = 180
Solving for variable 'x'.
Reorder the terms:
21 + -180 + 3x + x2 = 180 + -180
Combine like terms: 21 + -180 = -159
-159 + 3x + x2 = 180 + -180
Combine like terms: 180 + -180 = 0
-159 + 3x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '159' to each side of the equation.
-159 + 3x + 159 + x2 = 0 + 159
Reorder the terms:
-159 + 159 + 3x + x2 = 0 + 159
Combine like terms: -159 + 159 = 0
0 + 3x + x2 = 0 + 159
3x + x2 = 0 + 159
Combine like terms: 0 + 159 = 159
3x + x2 = 159
The x term is 3x. Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.
Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 159 + 2.25
Reorder the terms:
2.25 + 3x + x2 = 159 + 2.25
Combine like terms: 159 + 2.25 = 161.25
2.25 + 3x + x2 = 161.25
Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 161.25
Calculate the square root of the right side: 12.698425099
Break this problem into two subproblems by setting 
(x + 1.5) equal to 12.698425099 and -12.698425099.

Subproblem 1

x + 1.5 = 12.698425099 Simplifying x + 1.5 = 12.698425099 Reorder the terms: 1.5 + x = 12.698425099 Solving 1.5 + x = 12.698425099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.698425099 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.698425099 + -1.5 x = 12.698425099 + -1.5 Combine like terms: 12.698425099 + -1.5 = 11.198425099 x = 11.198425099 Simplifying x = 11.198425099

Subproblem 2

x + 1.5 = -12.698425099 Simplifying x + 1.5 = -12.698425099 Reorder the terms: 1.5 + x = -12.698425099 Solving 1.5 + x = -12.698425099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.698425099 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.698425099 + -1.5 x = -12.698425099 + -1.5 Combine like terms: -12.698425099 + -1.5 = -14.198425099 x = -14.198425099 Simplifying x = -14.198425099

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.198425099, -14.198425099}

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