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Simplifying x2 + 9x + -224 = 0 Reorder the terms: -224 + 9x + x2 = 0 Solving -224 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + 9x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 9x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 9x + x2 = 0 + 224 9x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 9x + x2 = 224 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 = 224 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 224 + 20.25 Combine like terms: 224 + 20.25 = 244.25 20.25 + 9x + x2 = 244.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 244.25 Calculate the square root of the right side: 15.628499608 Break this problem into two subproblems by setting (x + 4.5) equal to 15.628499608 and -15.628499608.Subproblem 1
x + 4.5 = 15.628499608 Simplifying x + 4.5 = 15.628499608 Reorder the terms: 4.5 + x = 15.628499608 Solving 4.5 + x = 15.628499608 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 = 15.628499608 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 15.628499608 + -4.5 x = 15.628499608 + -4.5 Combine like terms: 15.628499608 + -4.5 = 11.128499608 x = 11.128499608 Simplifying x = 11.128499608Subproblem 2
x + 4.5 = -15.628499608 Simplifying x + 4.5 = -15.628499608 Reorder the terms: 4.5 + x = -15.628499608 Solving 4.5 + x = -15.628499608 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 = -15.628499608 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -15.628499608 + -4.5 x = -15.628499608 + -4.5 Combine like terms: -15.628499608 + -4.5 = -20.128499608 x = -20.128499608 Simplifying x = -20.128499608Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.128499608, -20.128499608}
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