.05(2x+2).25(3x-1)=15

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Solution for .05(2x+2).25(3x-1)=15 equation:


Simplifying
0.05(2x + 2) * 0.25(3x + -1) = 15

Reorder the terms:
0.05(2 + 2x) * 0.25(3x + -1) = 15

Reorder the terms:
0.05(2 + 2x) * 0.25(-1 + 3x) = 15

Reorder the terms for easier multiplication:
0.05 * 0.25(2 + 2x)(-1 + 3x) = 15

Multiply 0.05 * 0.25
0.0125(2 + 2x)(-1 + 3x) = 15

Multiply (2 + 2x) * (-1 + 3x)
0.0125(2(-1 + 3x) + 2x * (-1 + 3x)) = 15
0.0125((-1 * 2 + 3x * 2) + 2x * (-1 + 3x)) = 15
0.0125((-2 + 6x) + 2x * (-1 + 3x)) = 15
0.0125(-2 + 6x + (-1 * 2x + 3x * 2x)) = 15
0.0125(-2 + 6x + (-2x + 6x2)) = 15

Combine like terms: 6x + -2x = 4x
0.0125(-2 + 4x + 6x2) = 15
(-2 * 0.0125 + 4x * 0.0125 + 6x2 * 0.0125) = 15
(-0.025 + 0.05x + 0.075x2) = 15

Solving
-0.025 + 0.05x + 0.075x2 = 15

Solving for variable 'x'.

Reorder the terms:
-0.025 + -15 + 0.05x + 0.075x2 = 15 + -15

Combine like terms: -0.025 + -15 = -15.025
-15.025 + 0.05x + 0.075x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15.025 + 0.05x + 0.075x2 = 0

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

Divide each side by '0.075'.
-200.3333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '200.3333333' to each side of the equation.
-200.3333333 + 0.6666666667x + 200.3333333 + x2 = 0 + 200.3333333

Reorder the terms:
-200.3333333 + 200.3333333 + 0.6666666667x + x2 = 0 + 200.3333333

Combine like terms: -200.3333333 + 200.3333333 = 0.0000000
0.0000000 + 0.6666666667x + x2 = 0 + 200.3333333
0.6666666667x + x2 = 0 + 200.3333333

Combine like terms: 0 + 200.3333333 = 200.3333333
0.6666666667x + x2 = 200.3333333

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 = 200.3333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 200.3333333 + 0.1111111112

Combine like terms: 200.3333333 + 0.1111111112 = 200.4444444112
0.1111111112 + 0.6666666667x + x2 = 200.4444444112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 200.4444444112

Calculate the square root of the right side: 14.157840387

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 14.157840387 and -14.157840387.

Subproblem 1

x + 0.3333333334 = 14.157840387 Simplifying x + 0.3333333334 = 14.157840387 Reorder the terms: 0.3333333334 + x = 14.157840387 Solving 0.3333333334 + x = 14.157840387 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 = 14.157840387 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 14.157840387 + -0.3333333334 x = 14.157840387 + -0.3333333334 Combine like terms: 14.157840387 + -0.3333333334 = 13.8245070536 x = 13.8245070536 Simplifying x = 13.8245070536

Subproblem 2

x + 0.3333333334 = -14.157840387 Simplifying x + 0.3333333334 = -14.157840387 Reorder the terms: 0.3333333334 + x = -14.157840387 Solving 0.3333333334 + x = -14.157840387 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 = -14.157840387 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -14.157840387 + -0.3333333334 x = -14.157840387 + -0.3333333334 Combine like terms: -14.157840387 + -0.3333333334 = -14.4911737204 x = -14.4911737204 Simplifying x = -14.4911737204

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.8245070536, -14.4911737204}

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