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Simplifying x2 + -9x + -99 = 5 Reorder the terms: -99 + -9x + x2 = 5 Solving -99 + -9x + x2 = 5 Solving for variable 'x'. Reorder the terms: -99 + -5 + -9x + x2 = 5 + -5 Combine like terms: -99 + -5 = -104 -104 + -9x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -104 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -9x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + -9x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -9x + x2 = 0 + 104 -9x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 -9x + x2 = 104 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 = 104 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 104 + 20.25 Combine like terms: 104 + 20.25 = 124.25 20.25 + -9x + x2 = 124.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + -4.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + -4.5 = 11.146748405 Simplifying x + -4.5 = 11.146748405 Reorder the terms: -4.5 + x = 11.146748405 Solving -4.5 + x = 11.146748405 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 = 11.146748405 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 11.146748405 + 4.5 x = 11.146748405 + 4.5 Combine like terms: 11.146748405 + 4.5 = 15.646748405 x = 15.646748405 Simplifying x = 15.646748405Subproblem 2
x + -4.5 = -11.146748405 Simplifying x + -4.5 = -11.146748405 Reorder the terms: -4.5 + x = -11.146748405 Solving -4.5 + x = -11.146748405 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 = -11.146748405 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -11.146748405 + 4.5 x = -11.146748405 + 4.5 Combine like terms: -11.146748405 + 4.5 = -6.646748405 x = -6.646748405 Simplifying x = -6.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.646748405, -6.646748405}
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