2x^2+24x=12

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Solution for 2x^2+24x=12 equation:


Simplifying
2x2 + 24x = 12

Reorder the terms:
24x + 2x2 = 12

Solving
24x + 2x2 = 12

Solving for variable 'x'.

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

Combine like terms: 12 + -12 = 0
-12 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 12x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-6 + 12x + x2)' equal to zero and attempt to solve: Simplifying -6 + 12x + x2 = 0 Solving -6 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 12x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 12x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 12x + x2 = 0 + 6 12x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 12x + x2 = 6 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 6 + 36 Reorder the terms: 36 + 12x + x2 = 6 + 36 Combine like terms: 6 + 36 = 42 36 + 12x + x2 = 42 Factor a perfect square on the left side: (x + 6)(x + 6) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (x + 6) equal to 6.480740698 and -6.480740698.

Subproblem 1

x + 6 = 6.480740698 Simplifying x + 6 = 6.480740698 Reorder the terms: 6 + x = 6.480740698 Solving 6 + x = 6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.480740698 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.480740698 + -6 x = 6.480740698 + -6 Combine like terms: 6.480740698 + -6 = 0.480740698 x = 0.480740698 Simplifying x = 0.480740698

Subproblem 2

x + 6 = -6.480740698 Simplifying x + 6 = -6.480740698 Reorder the terms: 6 + x = -6.480740698 Solving 6 + x = -6.480740698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.480740698 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.480740698 + -6 x = -6.480740698 + -6 Combine like terms: -6.480740698 + -6 = -12.480740698 x = -12.480740698 Simplifying x = -12.480740698

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.480740698, -12.480740698}

Solution

x = {0.480740698, -12.480740698}

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