(3x+4)+(2x-3)(5x+1)=

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Solution for (3x+4)+(2x-3)(5x+1)= equation:


Simplifying
(3x + 4) + (2x + -3)(5x + 1) = 0

Reorder the terms:
(4 + 3x) + (2x + -3)(5x + 1) = 0

Remove parenthesis around (4 + 3x)
4 + 3x + (2x + -3)(5x + 1) = 0

Reorder the terms:
4 + 3x + (-3 + 2x)(5x + 1) = 0

Reorder the terms:
4 + 3x + (-3 + 2x)(1 + 5x) = 0

Multiply (-3 + 2x) * (1 + 5x)
4 + 3x + (-3(1 + 5x) + 2x * (1 + 5x)) = 0
4 + 3x + ((1 * -3 + 5x * -3) + 2x * (1 + 5x)) = 0
4 + 3x + ((-3 + -15x) + 2x * (1 + 5x)) = 0
4 + 3x + (-3 + -15x + (1 * 2x + 5x * 2x)) = 0
4 + 3x + (-3 + -15x + (2x + 10x2)) = 0

Combine like terms: -15x + 2x = -13x
4 + 3x + (-3 + -13x + 10x2) = 0

Reorder the terms:
4 + -3 + 3x + -13x + 10x2 = 0

Combine like terms: 4 + -3 = 1
1 + 3x + -13x + 10x2 = 0

Combine like terms: 3x + -13x = -10x
1 + -10x + 10x2 = 0

Solving
1 + -10x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
0.1 + -1x + x2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -1x + -0.1 + x2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + -1x + x2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -1x + x2 = 0.0 + -0.1
-1x + x2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
-1x + x2 = -0.1

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.1 + 0.25

Combine like terms: -0.1 + 0.25 = 0.15
0.25 + -1x + x2 = 0.15

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.15

Calculate the square root of the right side: 0.387298335

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.387298335 and -0.387298335.

Subproblem 1

x + -0.5 = 0.387298335 Simplifying x + -0.5 = 0.387298335 Reorder the terms: -0.5 + x = 0.387298335 Solving -0.5 + x = 0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.387298335 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.387298335 + 0.5 x = 0.387298335 + 0.5 Combine like terms: 0.387298335 + 0.5 = 0.887298335 x = 0.887298335 Simplifying x = 0.887298335

Subproblem 2

x + -0.5 = -0.387298335 Simplifying x + -0.5 = -0.387298335 Reorder the terms: -0.5 + x = -0.387298335 Solving -0.5 + x = -0.387298335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.387298335 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.387298335 + 0.5 x = -0.387298335 + 0.5 Combine like terms: -0.387298335 + 0.5 = 0.112701665 x = 0.112701665 Simplifying x = 0.112701665

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.887298335, 0.112701665}

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