5x^2=3-3x

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Solution for 5x^2=3-3x equation:


Simplifying
5x2 = 3 + -3x

Solving
5x2 = 3 + -3x

Solving for variable 'x'.

Reorder the terms:
-3 + 3x + 5x2 = 3 + -3x + -3 + 3x

Reorder the terms:
-3 + 3x + 5x2 = 3 + -3 + -3x + 3x

Combine like terms: 3 + -3 = 0
-3 + 3x + 5x2 = 0 + -3x + 3x
-3 + 3x + 5x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-3 + 3x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 0.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.6x + x2 = 0 + 0.6
0.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.6x + x2 = 0.6

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.6 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.6 + 0.09

Combine like terms: 0.6 + 0.09 = 0.69
0.09 + 0.6x + x2 = 0.69

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.69

Calculate the square root of the right side: 0.830662386

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.830662386 and -0.830662386.

Subproblem 1

x + 0.3 = 0.830662386 Simplifying x + 0.3 = 0.830662386 Reorder the terms: 0.3 + x = 0.830662386 Solving 0.3 + x = 0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.830662386 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.830662386 + -0.3 x = 0.830662386 + -0.3 Combine like terms: 0.830662386 + -0.3 = 0.530662386 x = 0.530662386 Simplifying x = 0.530662386

Subproblem 2

x + 0.3 = -0.830662386 Simplifying x + 0.3 = -0.830662386 Reorder the terms: 0.3 + x = -0.830662386 Solving 0.3 + x = -0.830662386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.830662386 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.830662386 + -0.3 x = -0.830662386 + -0.3 Combine like terms: -0.830662386 + -0.3 = -1.130662386 x = -1.130662386 Simplifying x = -1.130662386

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.530662386, -1.130662386}

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