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Simplifying 6x2 + -12x = 1 Reorder the terms: -12x + 6x2 = 1 Solving -12x + 6x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -12x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -2x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -2x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -2x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.1666666667 -2x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -2x + x2 = 0.1666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.1666666667 + 1 Reorder the terms: 1 + -2x + x2 = 0.1666666667 + 1 Combine like terms: 0.1666666667 + 1 = 1.1666666667 1 + -2x + x2 = 1.1666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.1666666667 Calculate the square root of the right side: 1.08012345 Break this problem into two subproblems by setting (x + -1) equal to 1.08012345 and -1.08012345.Subproblem 1
x + -1 = 1.08012345 Simplifying x + -1 = 1.08012345 Reorder the terms: -1 + x = 1.08012345 Solving -1 + x = 1.08012345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.08012345 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.08012345 + 1 x = 1.08012345 + 1 Combine like terms: 1.08012345 + 1 = 2.08012345 x = 2.08012345 Simplifying x = 2.08012345Subproblem 2
x + -1 = -1.08012345 Simplifying x + -1 = -1.08012345 Reorder the terms: -1 + x = -1.08012345 Solving -1 + x = -1.08012345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.08012345 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.08012345 + 1 x = -1.08012345 + 1 Combine like terms: -1.08012345 + 1 = -0.08012345 x = -0.08012345 Simplifying x = -0.08012345Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.08012345, -0.08012345}
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