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Simplifying 12x2 + -3x + -36 = 0 Reorder the terms: -36 + -3x + 12x2 = 0 Solving -36 + -3x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -1x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + -1x + 4x2)' equal to zero and attempt to solve: Simplifying -12 + -1x + 4x2 = 0 Solving -12 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + -0.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.25x + x2 = 0 + 3 -0.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.25x + x2 = 3 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 3 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 3 + 0.015625 Combine like terms: 3 + 0.015625 = 3.015625 0.015625 + -0.25x + x2 = 3.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + -0.125) equal to 1.736555499 and -1.736555499.Subproblem 1
x + -0.125 = 1.736555499 Simplifying x + -0.125 = 1.736555499 Reorder the terms: -0.125 + x = 1.736555499 Solving -0.125 + x = 1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.736555499 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.736555499 + 0.125 x = 1.736555499 + 0.125 Combine like terms: 1.736555499 + 0.125 = 1.861555499 x = 1.861555499 Simplifying x = 1.861555499Subproblem 2
x + -0.125 = -1.736555499 Simplifying x + -0.125 = -1.736555499 Reorder the terms: -0.125 + x = -1.736555499 Solving -0.125 + x = -1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.736555499 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.736555499 + 0.125 x = -1.736555499 + 0.125 Combine like terms: -1.736555499 + 0.125 = -1.611555499 x = -1.611555499 Simplifying x = -1.611555499Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.861555499, -1.611555499}Solution
x = {1.861555499, -1.611555499}
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