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Simplifying x2 + -9x = 110 Reorder the terms: -9x + x2 = 110 Solving -9x + x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + -9x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -9x + x2 = 0 Begin completing the square. 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 = 15.912712211 x = 15.912712211 Simplifying x = 15.912712211Subproblem 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 = -6.912712211 x = -6.912712211 Simplifying x = -6.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.912712211, -6.912712211}
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