(4x+3)*x=520

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Solution for (4x+3)*x=520 equation:


Simplifying
(4x + 3) * x = 520

Reorder the terms:
(3 + 4x) * x = 520

Reorder the terms for easier multiplication:
x(3 + 4x) = 520
(3 * x + 4x * x) = 520
(3x + 4x2) = 520

Solving
3x + 4x2 = 520

Solving for variable 'x'.

Reorder the terms:
-520 + 3x + 4x2 = 520 + -520

Combine like terms: 520 + -520 = 0
-520 + 3x + 4x2 = 0

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

Divide each side by '4'.
-130 + 0.75x + x2 = 0

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 0.75x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 0.75x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 0.75x + x2 = 0 + 130
0.75x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
0.75x + x2 = 130

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 130 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 130 + 0.140625

Combine like terms: 130 + 0.140625 = 130.140625
0.140625 + 0.75x + x2 = 130.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 130.140625

Calculate the square root of the right side: 11.407919398

Break this problem into two subproblems by setting 
(x + 0.375) equal to 11.407919398 and -11.407919398.

Subproblem 1

x + 0.375 = 11.407919398 Simplifying x + 0.375 = 11.407919398 Reorder the terms: 0.375 + x = 11.407919398 Solving 0.375 + x = 11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 11.407919398 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 11.407919398 + -0.375 x = 11.407919398 + -0.375 Combine like terms: 11.407919398 + -0.375 = 11.032919398 x = 11.032919398 Simplifying x = 11.032919398

Subproblem 2

x + 0.375 = -11.407919398 Simplifying x + 0.375 = -11.407919398 Reorder the terms: 0.375 + x = -11.407919398 Solving 0.375 + x = -11.407919398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -11.407919398 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -11.407919398 + -0.375 x = -11.407919398 + -0.375 Combine like terms: -11.407919398 + -0.375 = -11.782919398 x = -11.782919398 Simplifying x = -11.782919398

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.032919398, -11.782919398}

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