-36x^2-24x+3=0

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Solution for -36x^2-24x+3=0 equation:


Simplifying
-36x2 + -24x + 3 = 0

Reorder the terms:
3 + -24x + -36x2 = 0

Solving
3 + -24x + -36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -8x + -12x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + -8x + -12x2)' equal to zero and attempt to solve: Simplifying 1 + -8x + -12x2 = 0 Solving 1 + -8x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.08333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.6666666667x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.6666666667x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.6666666667x + x2 = 0 + 0.08333333333 0.6666666667x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.6666666667x + x2 = 0.08333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.08333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.08333333333 + 0.1111111112 Combine like terms: 0.08333333333 + 0.1111111112 = 0.19444444453 0.1111111112 + 0.6666666667x + x2 = 0.19444444453 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.19444444453 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.440958552 and -0.440958552.

Subproblem 1

x + 0.3333333334 = 0.440958552 Simplifying x + 0.3333333334 = 0.440958552 Reorder the terms: 0.3333333334 + x = 0.440958552 Solving 0.3333333334 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.440958552 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.440958552 + -0.3333333334 x = 0.440958552 + -0.3333333334 Combine like terms: 0.440958552 + -0.3333333334 = 0.1076252186 x = 0.1076252186 Simplifying x = 0.1076252186

Subproblem 2

x + 0.3333333334 = -0.440958552 Simplifying x + 0.3333333334 = -0.440958552 Reorder the terms: 0.3333333334 + x = -0.440958552 Solving 0.3333333334 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.440958552 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.440958552 + -0.3333333334 x = -0.440958552 + -0.3333333334 Combine like terms: -0.440958552 + -0.3333333334 = -0.7742918854 x = -0.7742918854 Simplifying x = -0.7742918854

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1076252186, -0.7742918854}

Solution

x = {0.1076252186, -0.7742918854}

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