x^2+3x=196

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Solution for x^2+3x=196 equation:


Simplifying
x2 + 3x = 196

Reorder the terms:
3x + x2 = 196

Solving
3x + x2 = 196

Solving for variable 'x'.

Reorder the terms:
-196 + 3x + x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-196 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + 3x + 196 + x2 = 0 + 196

Reorder the terms:
-196 + 196 + 3x + x2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + 3x + x2 = 0 + 196
3x + x2 = 0 + 196

Combine like terms: 0 + 196 = 196
3x + x2 = 196

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 = 196 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 196 + 2.25

Combine like terms: 196 + 2.25 = 198.25
2.25 + 3x + x2 = 198.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 198.25

Calculate the square root of the right side: 14.08012784

Break this problem into two subproblems by setting 
(x + 1.5) equal to 14.08012784 and -14.08012784.

Subproblem 1

x + 1.5 = 14.08012784 Simplifying x + 1.5 = 14.08012784 Reorder the terms: 1.5 + x = 14.08012784 Solving 1.5 + x = 14.08012784 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 = 14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.08012784 + -1.5 x = 14.08012784 + -1.5 Combine like terms: 14.08012784 + -1.5 = 12.58012784 x = 12.58012784 Simplifying x = 12.58012784

Subproblem 2

x + 1.5 = -14.08012784 Simplifying x + 1.5 = -14.08012784 Reorder the terms: 1.5 + x = -14.08012784 Solving 1.5 + x = -14.08012784 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 = -14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.08012784 + -1.5 x = -14.08012784 + -1.5 Combine like terms: -14.08012784 + -1.5 = -15.58012784 x = -15.58012784 Simplifying x = -15.58012784

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.58012784, -15.58012784}

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