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Simplifying x2 + -9x = 1 Reorder the terms: -9x + x2 = 1 Solving -9x + x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -9x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -9x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -9x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -9x + x2 = 0 + 1 -9x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -9x + x2 = 1 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 = 1 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + -9x + x2 = 21.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -4.5 = 4.609772229 Simplifying x + -4.5 = 4.609772229 Reorder the terms: -4.5 + x = 4.609772229 Solving -4.5 + x = 4.609772229 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 = 4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.609772229 + 4.5 x = 4.609772229 + 4.5 Combine like terms: 4.609772229 + 4.5 = 9.109772229 x = 9.109772229 Simplifying x = 9.109772229Subproblem 2
x + -4.5 = -4.609772229 Simplifying x + -4.5 = -4.609772229 Reorder the terms: -4.5 + x = -4.609772229 Solving -4.5 + x = -4.609772229 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 = -4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.609772229 + 4.5 x = -4.609772229 + 4.5 Combine like terms: -4.609772229 + 4.5 = -0.109772229 x = -0.109772229 Simplifying x = -0.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.109772229, -0.109772229}
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