(x+6)2x-4=39*24

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Solution for (x+6)2x-4=39*24 equation:


Simplifying
(x + 6) * 2x + -4 = 39 * 24

Reorder the terms:
(6 + x) * 2x + -4 = 39 * 24

Reorder the terms for easier multiplication:
2x(6 + x) + -4 = 39 * 24
(6 * 2x + x * 2x) + -4 = 39 * 24
(12x + 2x2) + -4 = 39 * 24

Reorder the terms:
-4 + 12x + 2x2 = 39 * 24

Multiply 39 * 24
-4 + 12x + 2x2 = 936

Solving
-4 + 12x + 2x2 = 936

Solving for variable 'x'.

Reorder the terms:
-4 + -936 + 12x + 2x2 = 936 + -936

Combine like terms: -4 + -936 = -940
-940 + 12x + 2x2 = 936 + -936

Combine like terms: 936 + -936 = 0
-940 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-470 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-470 + 6x + x2)' equal to zero and attempt to solve: Simplifying -470 + 6x + x2 = 0 Solving -470 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '470' to each side of the equation. -470 + 6x + 470 + x2 = 0 + 470 Reorder the terms: -470 + 470 + 6x + x2 = 0 + 470 Combine like terms: -470 + 470 = 0 0 + 6x + x2 = 0 + 470 6x + x2 = 0 + 470 Combine like terms: 0 + 470 = 470 6x + x2 = 470 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 470 + 9 Reorder the terms: 9 + 6x + x2 = 470 + 9 Combine like terms: 470 + 9 = 479 9 + 6x + x2 = 479 Factor a perfect square on the left side: (x + 3)(x + 3) = 479 Calculate the square root of the right side: 21.886068628 Break this problem into two subproblems by setting (x + 3) equal to 21.886068628 and -21.886068628.

Subproblem 1

x + 3 = 21.886068628 Simplifying x + 3 = 21.886068628 Reorder the terms: 3 + x = 21.886068628 Solving 3 + x = 21.886068628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 21.886068628 + -3 Combine like terms: 3 + -3 = 0 0 + x = 21.886068628 + -3 x = 21.886068628 + -3 Combine like terms: 21.886068628 + -3 = 18.886068628 x = 18.886068628 Simplifying x = 18.886068628

Subproblem 2

x + 3 = -21.886068628 Simplifying x + 3 = -21.886068628 Reorder the terms: 3 + x = -21.886068628 Solving 3 + x = -21.886068628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -21.886068628 + -3 Combine like terms: 3 + -3 = 0 0 + x = -21.886068628 + -3 x = -21.886068628 + -3 Combine like terms: -21.886068628 + -3 = -24.886068628 x = -24.886068628 Simplifying x = -24.886068628

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.886068628, -24.886068628}

Solution

x = {18.886068628, -24.886068628}

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