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Simplifying -1x2 + -6x = -73 Reorder the terms: -6x + -1x2 = -73 Solving -6x + -1x2 = -73 Solving for variable 'x'. Reorder the terms: 73 + -6x + -1x2 = -73 + 73 Combine like terms: -73 + 73 = 0 73 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -73 + 6x + x2 = 0 Move the constant term to the right: Add '73' to each side of the equation. -73 + 6x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 6x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 6x + x2 = 0 + 73 6x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 6x + x2 = 73 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 = 73 + 9 Reorder the terms: 9 + 6x + x2 = 73 + 9 Combine like terms: 73 + 9 = 82 9 + 6x + x2 = 82 Factor a perfect square on the left side: (x + 3)(x + 3) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + 3) equal to 9.055385138 and -9.055385138.Subproblem 1
x + 3 = 9.055385138 Simplifying x + 3 = 9.055385138 Reorder the terms: 3 + x = 9.055385138 Solving 3 + x = 9.055385138 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 = 9.055385138 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.055385138 + -3 x = 9.055385138 + -3 Combine like terms: 9.055385138 + -3 = 6.055385138 x = 6.055385138 Simplifying x = 6.055385138Subproblem 2
x + 3 = -9.055385138 Simplifying x + 3 = -9.055385138 Reorder the terms: 3 + x = -9.055385138 Solving 3 + x = -9.055385138 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 = -9.055385138 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.055385138 + -3 x = -9.055385138 + -3 Combine like terms: -9.055385138 + -3 = -12.055385138 x = -12.055385138 Simplifying x = -12.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.055385138, -12.055385138}
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