x(2x)+3x=210

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Solution for x(2x)+3x=210 equation:


Simplifying
x(2x) + 3x = 210

Remove parenthesis around (2x)
x * 2x + 3x = 210

Reorder the terms for easier multiplication:
2x * x + 3x = 210

Multiply x * x
2x2 + 3x = 210

Reorder the terms:
3x + 2x2 = 210

Solving
3x + 2x2 = 210

Solving for variable 'x'.

Reorder the terms:
-210 + 3x + 2x2 = 210 + -210

Combine like terms: 210 + -210 = 0
-210 + 3x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-105 + 1.5x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 1.5x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 1.5x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 1.5x + x2 = 0 + 105
1.5x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
1.5x + x2 = 105

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 105 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 105 + 0.5625

Combine like terms: 105 + 0.5625 = 105.5625
0.5625 + 1.5x + x2 = 105.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 105.5625

Calculate the square root of the right side: 10.274361294

Break this problem into two subproblems by setting 
(x + 0.75) equal to 10.274361294 and -10.274361294.

Subproblem 1

x + 0.75 = 10.274361294 Simplifying x + 0.75 = 10.274361294 Reorder the terms: 0.75 + x = 10.274361294 Solving 0.75 + x = 10.274361294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 10.274361294 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 10.274361294 + -0.75 x = 10.274361294 + -0.75 Combine like terms: 10.274361294 + -0.75 = 9.524361294 x = 9.524361294 Simplifying x = 9.524361294

Subproblem 2

x + 0.75 = -10.274361294 Simplifying x + 0.75 = -10.274361294 Reorder the terms: 0.75 + x = -10.274361294 Solving 0.75 + x = -10.274361294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -10.274361294 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -10.274361294 + -0.75 x = -10.274361294 + -0.75 Combine like terms: -10.274361294 + -0.75 = -11.024361294 x = -11.024361294 Simplifying x = -11.024361294

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.524361294, -11.024361294}

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