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Simplifying 9x + x2 + -20 = 0 Reorder the terms: -20 + 9x + x2 = 0 Solving -20 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 9x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 9x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 9x + x2 = 0 + 20 9x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 9x + x2 = 20 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 = 20 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 20 + 20.25 Combine like terms: 20 + 20.25 = 40.25 20.25 + 9x + x2 = 40.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 4.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 4.5 = 6.34428877 Simplifying x + 4.5 = 6.34428877 Reorder the terms: 4.5 + x = 6.34428877 Solving 4.5 + x = 6.34428877 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 = 6.34428877 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.34428877 + -4.5 x = 6.34428877 + -4.5 Combine like terms: 6.34428877 + -4.5 = 1.84428877 x = 1.84428877 Simplifying x = 1.84428877Subproblem 2
x + 4.5 = -6.34428877 Simplifying x + 4.5 = -6.34428877 Reorder the terms: 4.5 + x = -6.34428877 Solving 4.5 + x = -6.34428877 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 = -6.34428877 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.34428877 + -4.5 x = -6.34428877 + -4.5 Combine like terms: -6.34428877 + -4.5 = -10.84428877 x = -10.84428877 Simplifying x = -10.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.84428877, -10.84428877}
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