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Simplifying 0 = -2x2 + -12x + 1 Reorder the terms: 0 = 1 + -12x + -2x2 Solving 0 = 1 + -12x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 12x + 2x2 = 1 + -12x + -2x2 + -1 + 12x + 2x2 Reorder the terms: -1 + 12x + 2x2 = 1 + -1 + -12x + 12x + -2x2 + 2x2 Combine like terms: 1 + -1 = 0 -1 + 12x + 2x2 = 0 + -12x + 12x + -2x2 + 2x2 -1 + 12x + 2x2 = -12x + 12x + -2x2 + 2x2 Combine like terms: -12x + 12x = 0 -1 + 12x + 2x2 = 0 + -2x2 + 2x2 -1 + 12x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -1 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 6x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 6x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 6x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 6x + x2 = 0 + 0.5 6x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 6x + x2 = 0.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 0.5 + 9 Reorder the terms: 9 + 6x + x2 = 0.5 + 9 Combine like terms: 0.5 + 9 = 9.5 9 + 6x + x2 = 9.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + 3) equal to 3.082207001 and -3.082207001.Subproblem 1
x + 3 = 3.082207001 Simplifying x + 3 = 3.082207001 Reorder the terms: 3 + x = 3.082207001 Solving 3 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.082207001 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.082207001 + -3 x = 3.082207001 + -3 Combine like terms: 3.082207001 + -3 = 0.082207001 x = 0.082207001 Simplifying x = 0.082207001Subproblem 2
x + 3 = -3.082207001 Simplifying x + 3 = -3.082207001 Reorder the terms: 3 + x = -3.082207001 Solving 3 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.082207001 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.082207001 + -3 x = -3.082207001 + -3 Combine like terms: -3.082207001 + -3 = -6.082207001 x = -6.082207001 Simplifying x = -6.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.082207001, -6.082207001}
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