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Simplifying 0 = 6x + x2 + -77 Reorder the terms: 0 = -77 + 6x + x2 Solving 0 = -77 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + 77 = 77 77 + -6x + -1x2 = -77 + 6x + x2 + 77 + -6x + -1x2 Reorder the terms: 77 + -6x + -1x2 = -77 + 77 + 6x + -6x + x2 + -1x2 Combine like terms: -77 + 77 = 0 77 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 77 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 77 + -6x + -1x2 = 0 + x2 + -1x2 77 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 77 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -77 + 6x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + 6x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 6x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 6x + x2 = 0 + 77 6x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 6x + x2 = 77 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 = 77 + 9 Reorder the terms: 9 + 6x + x2 = 77 + 9 Combine like terms: 77 + 9 = 86 9 + 6x + x2 = 86 Factor a perfect square on the left side: (x + 3)(x + 3) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 3) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 3 = 9.273618495 Simplifying x + 3 = 9.273618495 Reorder the terms: 3 + x = 9.273618495 Solving 3 + x = 9.273618495 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 = 9.273618495 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.273618495 + -3 x = 9.273618495 + -3 Combine like terms: 9.273618495 + -3 = 6.273618495 x = 6.273618495 Simplifying x = 6.273618495Subproblem 2
x + 3 = -9.273618495 Simplifying x + 3 = -9.273618495 Reorder the terms: 3 + x = -9.273618495 Solving 3 + x = -9.273618495 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 = -9.273618495 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.273618495 + -3 x = -9.273618495 + -3 Combine like terms: -9.273618495 + -3 = -12.273618495 x = -12.273618495 Simplifying x = -12.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.273618495, -12.273618495}
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