-15x^2=12x-5

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Solution for -15x^2=12x-5 equation:


Simplifying
-15x2 = 12x + -5

Reorder the terms:
-15x2 = -5 + 12x

Solving
-15x2 = -5 + 12x

Solving for variable 'x'.

Reorder the terms:
5 + -12x + -15x2 = -5 + 12x + 5 + -12x

Reorder the terms:
5 + -12x + -15x2 = -5 + 5 + 12x + -12x

Combine like terms: -5 + 5 = 0
5 + -12x + -15x2 = 0 + 12x + -12x
5 + -12x + -15x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
5 + -12x + -15x2 = 0

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

Divide each side by '-15'.
-0.3333333333 + 0.8x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.8x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.8x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.8x + x2 = 0 + 0.3333333333
0.8x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.8x + x2 = 0.3333333333

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.3333333333 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.3333333333 + 0.16

Combine like terms: 0.3333333333 + 0.16 = 0.4933333333
0.16 + 0.8x + x2 = 0.4933333333

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.4933333333

Calculate the square root of the right side: 0.702376917

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.702376917 and -0.702376917.

Subproblem 1

x + 0.4 = 0.702376917 Simplifying x + 0.4 = 0.702376917 Reorder the terms: 0.4 + x = 0.702376917 Solving 0.4 + x = 0.702376917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.702376917 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.702376917 + -0.4 x = 0.702376917 + -0.4 Combine like terms: 0.702376917 + -0.4 = 0.302376917 x = 0.302376917 Simplifying x = 0.302376917

Subproblem 2

x + 0.4 = -0.702376917 Simplifying x + 0.4 = -0.702376917 Reorder the terms: 0.4 + x = -0.702376917 Solving 0.4 + x = -0.702376917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.702376917 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.702376917 + -0.4 x = -0.702376917 + -0.4 Combine like terms: -0.702376917 + -0.4 = -1.102376917 x = -1.102376917 Simplifying x = -1.102376917

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.302376917, -1.102376917}

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