1.5x^2+0.7x=0.048

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Solution for 1.5x^2+0.7x=0.048 equation: 


Simplifying
1.5x2 + 0.7x = 0.048

Reorder the terms:
0.7x + 1.5x2 = 0.048

Solving
0.7x + 1.5x2 = 0.048

Solving for variable 'x'.

Reorder the terms:
-0.048 + 0.7x + 1.5x2 = 0.048 + -0.048

Combine like terms: 0.048 + -0.048 = 0.000
-0.048 + 0.7x + 1.5x2 = 0.000

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

Divide each side by '1.5'.
-0.032 + 0.4666666667x + x2 = 0.00

Move the constant term to the right:

Add '0.032' to each side of the equation.
-0.032 + 0.4666666667x + 0.032 + x2 = 0.00 + 0.032

Reorder the terms:
-0.032 + 0.032 + 0.4666666667x + x2 = 0.00 + 0.032

Combine like terms: -0.032 + 0.032 = 0.000
0.000 + 0.4666666667x + x2 = 0.00 + 0.032
0.4666666667x + x2 = 0.00 + 0.032

Combine like terms: 0.00 + 0.032 = 0.032
0.4666666667x + x2 = 0.032

The x term is 0.4666666667x.  Take half its coefficient (0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
0.4666666667x + 0.05444444448 + x2 = 0.032 + 0.05444444448

Reorder the terms:
0.05444444448 + 0.4666666667x + x2 = 0.032 + 0.05444444448

Combine like terms: 0.032 + 0.05444444448 = 0.08644444448
0.05444444448 + 0.4666666667x + x2 = 0.08644444448

Factor a perfect square on the left side:
(x + 0.2333333334)(x + 0.2333333334) = 0.08644444448

Calculate the square root of the right side: 0.294014361

Break this problem into two subproblems by setting 
(x + 0.2333333334) equal to 0.294014361 and -0.294014361.


Subproblem 1
x + 0.2333333334 = 0.294014361

Simplifying
x + 0.2333333334 = 0.294014361

Reorder the terms:
0.2333333334 + x = 0.294014361

Solving
0.2333333334 + x = 0.294014361

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = 0.294014361 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = 0.294014361 + -0.2333333334
x = 0.294014361 + -0.2333333334

Combine like terms: 0.294014361 + -0.2333333334 = 0.0606810276
x = 0.0606810276

Simplifying
x = 0.0606810276


Subproblem 2
x + 0.2333333334 = -0.294014361

Simplifying
x + 0.2333333334 = -0.294014361

Reorder the terms:
0.2333333334 + x = -0.294014361

Solving
0.2333333334 + x = -0.294014361

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2333333334' to each side of the equation.
0.2333333334 + -0.2333333334 + x = -0.294014361 + -0.2333333334

Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000
0.0000000000 + x = -0.294014361 + -0.2333333334
x = -0.294014361 + -0.2333333334

Combine like terms: -0.294014361 + -0.2333333334 = -0.5273476944
x = -0.5273476944

Simplifying
x = -0.5273476944


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0606810276, -0.5273476944}

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