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Simplifying 12x2 + -36x + 4 = 0 Reorder the terms: 4 + -36x + 12x2 = 0 Solving 4 + -36x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -9x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -9x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -9x + 3x2 = 0 Solving 1 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -3x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -3x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -3x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.3333333333 -3x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -3x + x2 = -0.3333333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.3333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.3333333333 + 2.25 Combine like terms: -0.3333333333 + 2.25 = 1.9166666667 2.25 + -3x + x2 = 1.9166666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.9166666667 Calculate the square root of the right side: 1.38443731 Break this problem into two subproblems by setting (x + -1.5) equal to 1.38443731 and -1.38443731.Subproblem 1
x + -1.5 = 1.38443731 Simplifying x + -1.5 = 1.38443731 Reorder the terms: -1.5 + x = 1.38443731 Solving -1.5 + x = 1.38443731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.38443731 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.38443731 + 1.5 x = 1.38443731 + 1.5 Combine like terms: 1.38443731 + 1.5 = 2.88443731 x = 2.88443731 Simplifying x = 2.88443731Subproblem 2
x + -1.5 = -1.38443731 Simplifying x + -1.5 = -1.38443731 Reorder the terms: -1.5 + x = -1.38443731 Solving -1.5 + x = -1.38443731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.38443731 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.38443731 + 1.5 x = -1.38443731 + 1.5 Combine like terms: -1.38443731 + 1.5 = 0.11556269 x = 0.11556269 Simplifying x = 0.11556269Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.88443731, 0.11556269}Solution
x = {2.88443731, 0.11556269}
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