x^2+3x=144

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Solution for x^2+3x=144 equation:


Simplifying
x2 + 3x = 144

Reorder the terms:
3x + x2 = 144

Solving
3x + x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + 3x + x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 3x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 3x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 3x + x2 = 0 + 144
3x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
3x + x2 = 144

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 = 144 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 144 + 2.25

Combine like terms: 144 + 2.25 = 146.25
2.25 + 3x + x2 = 146.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + 1.5) equal to 12.093386622 and -12.093386622.

Subproblem 1

x + 1.5 = 12.093386622 Simplifying x + 1.5 = 12.093386622 Reorder the terms: 1.5 + x = 12.093386622 Solving 1.5 + x = 12.093386622 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 = 12.093386622 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.093386622 + -1.5 x = 12.093386622 + -1.5 Combine like terms: 12.093386622 + -1.5 = 10.593386622 x = 10.593386622 Simplifying x = 10.593386622

Subproblem 2

x + 1.5 = -12.093386622 Simplifying x + 1.5 = -12.093386622 Reorder the terms: 1.5 + x = -12.093386622 Solving 1.5 + x = -12.093386622 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 = -12.093386622 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.093386622 + -1.5 x = -12.093386622 + -1.5 Combine like terms: -12.093386622 + -1.5 = -13.593386622 x = -13.593386622 Simplifying x = -13.593386622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.593386622, -13.593386622}

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