24x+4x^2-12=0

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Solution for 24x+4x^2-12=0 equation:


Simplifying
24x + 4x2 + -12 = 0

Reorder the terms:
-12 + 24x + 4x2 = 0

Solving
-12 + 24x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 6x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + 6x + x2)' equal to zero and attempt to solve: Simplifying -3 + 6x + x2 = 0 Solving -3 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6x + x2 = 0 + 3 6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 6x + x2 = 3 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 = 3 + 9 Reorder the terms: 9 + 6x + x2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6x + x2 = 12 Factor a perfect square on the left side: (x + 3)(x + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + 3 = 3.464101615 Simplifying x + 3 = 3.464101615 Reorder the terms: 3 + x = 3.464101615 Solving 3 + x = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.464101615 + -3 x = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 x = 0.464101615 Simplifying x = 0.464101615

Subproblem 2

x + 3 = -3.464101615 Simplifying x + 3 = -3.464101615 Reorder the terms: 3 + x = -3.464101615 Solving 3 + x = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.464101615 + -3 x = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 x = -6.464101615 Simplifying x = -6.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.464101615, -6.464101615}

Solution

x = {0.464101615, -6.464101615}

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