3x(4+4x)-1=47

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Solution for 3x(4+4x)-1=47 equation:


Simplifying
3x(4 + 4x) + -1 = 47
(4 * 3x + 4x * 3x) + -1 = 47
(12x + 12x2) + -1 = 47

Reorder the terms:
-1 + 12x + 12x2 = 47

Solving
-1 + 12x + 12x2 = 47

Solving for variable 'x'.

Reorder the terms:
-1 + -47 + 12x + 12x2 = 47 + -47

Combine like terms: -1 + -47 = -48
-48 + 12x + 12x2 = 47 + -47

Combine like terms: 47 + -47 = 0
-48 + 12x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-4 + x + x2) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(-4 + x + x2)' equal to zero and attempt to solve: Simplifying -4 + x + x2 = 0 Solving -4 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x + x2 = 0 + 4 x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 x + x2 = 4 The x term is x. 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. x + 0.25 + x2 = 4 + 0.25 Reorder the terms: 0.25 + x + x2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + x + x2 = 4.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + 0.5 = 2.061552813 Simplifying x + 0.5 = 2.061552813 Reorder the terms: 0.5 + x = 2.061552813 Solving 0.5 + x = 2.061552813 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 = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.061552813 + -0.5 x = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 x = 1.561552813 Simplifying x = 1.561552813

Subproblem 2

x + 0.5 = -2.061552813 Simplifying x + 0.5 = -2.061552813 Reorder the terms: 0.5 + x = -2.061552813 Solving 0.5 + x = -2.061552813 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 = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.061552813 + -0.5 x = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 x = -2.561552813 Simplifying x = -2.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.561552813, -2.561552813}

Solution

x = {1.561552813, -2.561552813}

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