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Simplifying 12x2 + -6x = 58 Reorder the terms: -6x + 12x2 = 58 Solving -6x + 12x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + -6x + 12x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -6x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-29 + -3x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-29 + -3x + 6x2)' equal to zero and attempt to solve: Simplifying -29 + -3x + 6x2 = 0 Solving -29 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.833333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.833333333' to each side of the equation. -4.833333333 + -0.5x + 4.833333333 + x2 = 0 + 4.833333333 Reorder the terms: -4.833333333 + 4.833333333 + -0.5x + x2 = 0 + 4.833333333 Combine like terms: -4.833333333 + 4.833333333 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 4.833333333 -0.5x + x2 = 0 + 4.833333333 Combine like terms: 0 + 4.833333333 = 4.833333333 -0.5x + x2 = 4.833333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4.833333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4.833333333 + 0.0625 Combine like terms: 4.833333333 + 0.0625 = 4.895833333 0.0625 + -0.5x + x2 = 4.895833333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.895833333 Calculate the square root of the right side: 2.212653008 Break this problem into two subproblems by setting (x + -0.25) equal to 2.212653008 and -2.212653008.Subproblem 1
x + -0.25 = 2.212653008 Simplifying x + -0.25 = 2.212653008 Reorder the terms: -0.25 + x = 2.212653008 Solving -0.25 + x = 2.212653008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.212653008 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.212653008 + 0.25 x = 2.212653008 + 0.25 Combine like terms: 2.212653008 + 0.25 = 2.462653008 x = 2.462653008 Simplifying x = 2.462653008Subproblem 2
x + -0.25 = -2.212653008 Simplifying x + -0.25 = -2.212653008 Reorder the terms: -0.25 + x = -2.212653008 Solving -0.25 + x = -2.212653008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.212653008 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.212653008 + 0.25 x = -2.212653008 + 0.25 Combine like terms: -2.212653008 + 0.25 = -1.962653008 x = -1.962653008 Simplifying x = -1.962653008Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.462653008, -1.962653008}Solution
x = {2.462653008, -1.962653008}
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