0=12x^2-24x-9

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Solution for 0=12x^2-24x-9 equation:


Simplifying
0 = 12x2 + -24x + -9

Reorder the terms:
0 = -9 + -24x + 12x2

Solving
0 = -9 + -24x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 9 = 9
9 + 24x + -12x2 = -9 + -24x + 12x2 + 9 + 24x + -12x2

Reorder the terms:
9 + 24x + -12x2 = -9 + 9 + -24x + 24x + 12x2 + -12x2

Combine like terms: -9 + 9 = 0
9 + 24x + -12x2 = 0 + -24x + 24x + 12x2 + -12x2
9 + 24x + -12x2 = -24x + 24x + 12x2 + -12x2

Combine like terms: -24x + 24x = 0
9 + 24x + -12x2 = 0 + 12x2 + -12x2
9 + 24x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
9 + 24x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 8x + -4x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(3 + 8x + -4x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + -4x2 = 0 Solving 3 + 8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -2x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2x + x2 = 0 + 0.75 -2x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2x + x2 = 0.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.75 + 1 Reorder the terms: 1 + -2x + x2 = 0.75 + 1 Combine like terms: 0.75 + 1 = 1.75 1 + -2x + x2 = 1.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -1) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -1 = 1.322875656 Simplifying x + -1 = 1.322875656 Reorder the terms: -1 + x = 1.322875656 Solving -1 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.322875656 + 1 x = 1.322875656 + 1 Combine like terms: 1.322875656 + 1 = 2.322875656 x = 2.322875656 Simplifying x = 2.322875656

Subproblem 2

x + -1 = -1.322875656 Simplifying x + -1 = -1.322875656 Reorder the terms: -1 + x = -1.322875656 Solving -1 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.322875656 + 1 x = -1.322875656 + 1 Combine like terms: -1.322875656 + 1 = -0.322875656 x = -0.322875656 Simplifying x = -0.322875656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.322875656, -0.322875656}

Solution

x = {2.322875656, -0.322875656}

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