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Simplifying 0 = x2 + 9x + -110 Reorder the terms: 0 = -110 + 9x + x2 Solving 0 = -110 + 9x + x2 Solving for variable 'x'. Combine like terms: 0 + 110 = 110 110 + -9x + -1x2 = -110 + 9x + x2 + 110 + -9x + -1x2 Reorder the terms: 110 + -9x + -1x2 = -110 + 110 + 9x + -9x + x2 + -1x2 Combine like terms: -110 + 110 = 0 110 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2 110 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 110 + -9x + -1x2 = 0 + x2 + -1x2 110 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 110 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110 + 9x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 9x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 9x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 9x + x2 = 0 + 110 9x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 9x + x2 = 110 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 110 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 110 + 20.25 Combine like terms: 110 + 20.25 = 130.25 20.25 + 9x + x2 = 130.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 4.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 4.5 = 11.412712211 Simplifying x + 4.5 = 11.412712211 Reorder the terms: 4.5 + x = 11.412712211 Solving 4.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 11.412712211 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.412712211 + -4.5 x = 11.412712211 + -4.5 Combine like terms: 11.412712211 + -4.5 = 6.912712211 x = 6.912712211 Simplifying x = 6.912712211Subproblem 2
x + 4.5 = -11.412712211 Simplifying x + 4.5 = -11.412712211 Reorder the terms: 4.5 + x = -11.412712211 Solving 4.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -11.412712211 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.412712211 + -4.5 x = -11.412712211 + -4.5 Combine like terms: -11.412712211 + -4.5 = -15.912712211 x = -15.912712211 Simplifying x = -15.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.912712211, -15.912712211}
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