70=x+x+x(3*x)

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Solution for 70=x+x+x(3*x) equation:


Simplifying
70 = x + x + x(3x)

Remove parenthesis around (3x)
70 = x + x + x * 3x

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

Multiply x * x
70 = x + x + 3x2

Combine like terms: x + x = 2x
70 = 2x + 3x2

Solving
70 = 2x + 3x2

Solving for variable 'x'.

Reorder the terms:
70 + -2x + -3x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
70 + -2x + -3x2 = 0 + 3x2 + -3x2
70 + -2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
70 + -2x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-23.33333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + 0.6666666667x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + 0.6666666667x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + 0.6666666667x + x2 = 0 + 23.33333333
0.6666666667x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
0.6666666667x + x2 = 23.33333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 23.33333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 23.33333333 + 0.1111111112

Combine like terms: 23.33333333 + 0.1111111112 = 23.4444444412
0.1111111112 + 0.6666666667x + x2 = 23.4444444412

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 23.4444444412

Calculate the square root of the right side: 4.841946348

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 4.841946348 and -4.841946348.

Subproblem 1

x + 0.3333333334 = 4.841946348 Simplifying x + 0.3333333334 = 4.841946348 Reorder the terms: 0.3333333334 + x = 4.841946348 Solving 0.3333333334 + x = 4.841946348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 4.841946348 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 4.841946348 + -0.3333333334 x = 4.841946348 + -0.3333333334 Combine like terms: 4.841946348 + -0.3333333334 = 4.5086130146 x = 4.5086130146 Simplifying x = 4.5086130146

Subproblem 2

x + 0.3333333334 = -4.841946348 Simplifying x + 0.3333333334 = -4.841946348 Reorder the terms: 0.3333333334 + x = -4.841946348 Solving 0.3333333334 + x = -4.841946348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -4.841946348 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -4.841946348 + -0.3333333334 x = -4.841946348 + -0.3333333334 Combine like terms: -4.841946348 + -0.3333333334 = -5.1752796814 x = -5.1752796814 Simplifying x = -5.1752796814

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.5086130146, -5.1752796814}

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