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Simplifying 0 = x2 + -12x + 1 Reorder the terms: 0 = 1 + -12x + x2 Solving 0 = 1 + -12x + x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 12x + -1x2 = 1 + -12x + x2 + -1 + 12x + -1x2 Reorder the terms: -1 + 12x + -1x2 = 1 + -1 + -12x + 12x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -1 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -1 + 12x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -1 + 12x + -1x2 = 0 + x2 + -1x2 -1 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -12x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -12x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -12x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12x + x2 = 0 + -1 -12x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -12x + x2 = -1 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -1 + 36 Reorder the terms: 36 + -12x + x2 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + -12x + x2 = 35 Factor a perfect square on the left side: (x + -6)(x + -6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -6) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -6 = 5.916079783 Simplifying x + -6 = 5.916079783 Reorder the terms: -6 + x = 5.916079783 Solving -6 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.916079783 + 6 x = 5.916079783 + 6 Combine like terms: 5.916079783 + 6 = 11.916079783 x = 11.916079783 Simplifying x = 11.916079783Subproblem 2
x + -6 = -5.916079783 Simplifying x + -6 = -5.916079783 Reorder the terms: -6 + x = -5.916079783 Solving -6 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.916079783 + 6 x = -5.916079783 + 6 Combine like terms: -5.916079783 + 6 = 0.083920217 x = 0.083920217 Simplifying x = 0.083920217Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.916079783, 0.083920217}
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