3x(23+5x)=14

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Solution for 3x(23+5x)=14 equation:


Simplifying
3x(23 + 5x) = 14
(23 * 3x + 5x * 3x) = 14
(69x + 15x2) = 14

Solving
69x + 15x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 69x + 15x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 69x + 15x2 = 0

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

Divide each side by '15'.
-0.9333333333 + 4.6x + x2 = 0

Move the constant term to the right:

Add '0.9333333333' to each side of the equation.
-0.9333333333 + 4.6x + 0.9333333333 + x2 = 0 + 0.9333333333

Reorder the terms:
-0.9333333333 + 0.9333333333 + 4.6x + x2 = 0 + 0.9333333333

Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000
0.0000000000 + 4.6x + x2 = 0 + 0.9333333333
4.6x + x2 = 0 + 0.9333333333

Combine like terms: 0 + 0.9333333333 = 0.9333333333
4.6x + x2 = 0.9333333333

The x term is 4.6x.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6x + 5.29 + x2 = 0.9333333333 + 5.29

Reorder the terms:
5.29 + 4.6x + x2 = 0.9333333333 + 5.29

Combine like terms: 0.9333333333 + 5.29 = 6.2233333333
5.29 + 4.6x + x2 = 6.2233333333

Factor a perfect square on the left side:
(x + 2.3)(x + 2.3) = 6.2233333333

Calculate the square root of the right side: 2.494660966

Break this problem into two subproblems by setting 
(x + 2.3) equal to 2.494660966 and -2.494660966.

Subproblem 1

x + 2.3 = 2.494660966 Simplifying x + 2.3 = 2.494660966 Reorder the terms: 2.3 + x = 2.494660966 Solving 2.3 + x = 2.494660966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 2.494660966 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 2.494660966 + -2.3 x = 2.494660966 + -2.3 Combine like terms: 2.494660966 + -2.3 = 0.194660966 x = 0.194660966 Simplifying x = 0.194660966

Subproblem 2

x + 2.3 = -2.494660966 Simplifying x + 2.3 = -2.494660966 Reorder the terms: 2.3 + x = -2.494660966 Solving 2.3 + x = -2.494660966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -2.494660966 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -2.494660966 + -2.3 x = -2.494660966 + -2.3 Combine like terms: -2.494660966 + -2.3 = -4.794660966 x = -4.794660966 Simplifying x = -4.794660966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.194660966, -4.794660966}

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