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Simplifying 243 = 12x2 + -12x Reorder the terms: 243 = -12x + 12x2 Solving 243 = -12x + 12x2 Solving for variable 'x'. Reorder the terms: 243 + 12x + -12x2 = -12x + 12x + 12x2 + -12x2 Combine like terms: -12x + 12x = 0 243 + 12x + -12x2 = 0 + 12x2 + -12x2 243 + 12x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 243 + 12x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(81 + 4x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(81 + 4x + -4x2)' equal to zero and attempt to solve: Simplifying 81 + 4x + -4x2 = 0 Solving 81 + 4x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -20.25 + -1x + x2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -1x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -1x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -1x + x2 = 0 + 20.25 -1x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -1x + x2 = 20.25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 20.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 20.25 + 0.25 Combine like terms: 20.25 + 0.25 = 20.5 0.25 + -1x + x2 = 20.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (x + -0.5) equal to 4.527692569 and -4.527692569.Subproblem 1
x + -0.5 = 4.527692569 Simplifying x + -0.5 = 4.527692569 Reorder the terms: -0.5 + x = 4.527692569 Solving -0.5 + x = 4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.527692569 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.527692569 + 0.5 x = 4.527692569 + 0.5 Combine like terms: 4.527692569 + 0.5 = 5.027692569 x = 5.027692569 Simplifying x = 5.027692569Subproblem 2
x + -0.5 = -4.527692569 Simplifying x + -0.5 = -4.527692569 Reorder the terms: -0.5 + x = -4.527692569 Solving -0.5 + x = -4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.527692569 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.527692569 + 0.5 x = -4.527692569 + 0.5 Combine like terms: -4.527692569 + 0.5 = -4.027692569 x = -4.027692569 Simplifying x = -4.027692569Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.027692569, -4.027692569}Solution
x = {5.027692569, -4.027692569}
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