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Simplifying 1 = x2 + -12x + 20 Reorder the terms: 1 = 20 + -12x + x2 Solving 1 = 20 + -12x + x2 Solving for variable 'x'. Combine like terms: 1 + -20 = -19 -19 + 12x + -1x2 = 20 + -12x + x2 + -20 + 12x + -1x2 Reorder the terms: -19 + 12x + -1x2 = 20 + -20 + -12x + 12x + x2 + -1x2 Combine like terms: 20 + -20 = 0 -19 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2 -19 + 12x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 -19 + 12x + -1x2 = 0 + x2 + -1x2 -19 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -19 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 19 + -12x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -12x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -12x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -12x + x2 = 0 + -19 -12x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -12x + x2 = -19 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 = -19 + 36 Reorder the terms: 36 + -12x + x2 = -19 + 36 Combine like terms: -19 + 36 = 17 36 + -12x + x2 = 17 Factor a perfect square on the left side: (x + -6)(x + -6) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -6) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -6 = 4.123105626 Simplifying x + -6 = 4.123105626 Reorder the terms: -6 + x = 4.123105626 Solving -6 + x = 4.123105626 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 = 4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.123105626 + 6 x = 4.123105626 + 6 Combine like terms: 4.123105626 + 6 = 10.123105626 x = 10.123105626 Simplifying x = 10.123105626Subproblem 2
x + -6 = -4.123105626 Simplifying x + -6 = -4.123105626 Reorder the terms: -6 + x = -4.123105626 Solving -6 + x = -4.123105626 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 = -4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.123105626 + 6 x = -4.123105626 + 6 Combine like terms: -4.123105626 + 6 = 1.876894374 x = 1.876894374 Simplifying x = 1.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.123105626, 1.876894374}
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