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Simplifying (6x + 12x2 + -17) = 0 Reorder the terms: (-17 + 6x + 12x2) = 0 Remove parenthesis around (-17 + 6x + 12x2) -17 + 6x + 12x2 = 0 Solving -17 + 6x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.416666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.416666667' to each side of the equation. -1.416666667 + 0.5x + 1.416666667 + x2 = 0 + 1.416666667 Reorder the terms: -1.416666667 + 1.416666667 + 0.5x + x2 = 0 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 1.416666667 0.5x + x2 = 0 + 1.416666667 Combine like terms: 0 + 1.416666667 = 1.416666667 0.5x + x2 = 1.416666667 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 = 1.416666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.416666667 + 0.0625 Combine like terms: 1.416666667 + 0.0625 = 1.479166667 0.0625 + 0.5x + x2 = 1.479166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.479166667 Calculate the square root of the right side: 1.21620996 Break this problem into two subproblems by setting (x + 0.25) equal to 1.21620996 and -1.21620996.Subproblem 1
x + 0.25 = 1.21620996 Simplifying x + 0.25 = 1.21620996 Reorder the terms: 0.25 + x = 1.21620996 Solving 0.25 + x = 1.21620996 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 = 1.21620996 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.21620996 + -0.25 x = 1.21620996 + -0.25 Combine like terms: 1.21620996 + -0.25 = 0.96620996 x = 0.96620996 Simplifying x = 0.96620996Subproblem 2
x + 0.25 = -1.21620996 Simplifying x + 0.25 = -1.21620996 Reorder the terms: 0.25 + x = -1.21620996 Solving 0.25 + x = -1.21620996 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 = -1.21620996 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.21620996 + -0.25 x = -1.21620996 + -0.25 Combine like terms: -1.21620996 + -0.25 = -1.46620996 x = -1.46620996 Simplifying x = -1.46620996Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96620996, -1.46620996}
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