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Simplifying x2 + 15x + -224 = 0 Reorder the terms: -224 + 15x + x2 = 0 Solving -224 + 15x + 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 + 15x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 15x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 15x + x2 = 0 + 224 15x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 15x + x2 = 224 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 224 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 224 + 56.25 Combine like terms: 224 + 56.25 = 280.25 56.25 + 15x + x2 = 280.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 280.25 Calculate the square root of the right side: 16.740669043 Break this problem into two subproblems by setting (x + 7.5) equal to 16.740669043 and -16.740669043.Subproblem 1
x + 7.5 = 16.740669043 Simplifying x + 7.5 = 16.740669043 Reorder the terms: 7.5 + x = 16.740669043 Solving 7.5 + x = 16.740669043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 16.740669043 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 16.740669043 + -7.5 x = 16.740669043 + -7.5 Combine like terms: 16.740669043 + -7.5 = 9.240669043 x = 9.240669043 Simplifying x = 9.240669043Subproblem 2
x + 7.5 = -16.740669043 Simplifying x + 7.5 = -16.740669043 Reorder the terms: 7.5 + x = -16.740669043 Solving 7.5 + x = -16.740669043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -16.740669043 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -16.740669043 + -7.5 x = -16.740669043 + -7.5 Combine like terms: -16.740669043 + -7.5 = -24.240669043 x = -24.240669043 Simplifying x = -24.240669043Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.240669043, -24.240669043}
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