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Simplifying x2 + -9x + 9 + -49 = 0 Reorder the terms: 9 + -49 + -9x + x2 = 0 Combine like terms: 9 + -49 = -40 -40 + -9x + x2 = 0 Solving -40 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -9x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -9x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -9x + x2 = 0 + 40 -9x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -9x + x2 = 40 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 = 40 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 40 + 20.25 Combine like terms: 40 + 20.25 = 60.25 20.25 + -9x + x2 = 60.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -4.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -4.5 = 7.762087348 Simplifying x + -4.5 = 7.762087348 Reorder the terms: -4.5 + x = 7.762087348 Solving -4.5 + x = 7.762087348 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 = 7.762087348 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.762087348 + 4.5 x = 7.762087348 + 4.5 Combine like terms: 7.762087348 + 4.5 = 12.262087348 x = 12.262087348 Simplifying x = 12.262087348Subproblem 2
x + -4.5 = -7.762087348 Simplifying x + -4.5 = -7.762087348 Reorder the terms: -4.5 + x = -7.762087348 Solving -4.5 + x = -7.762087348 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 = -7.762087348 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.762087348 + 4.5 x = -7.762087348 + 4.5 Combine like terms: -7.762087348 + 4.5 = -3.262087348 x = -3.262087348 Simplifying x = -3.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.262087348, -3.262087348}
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