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Simplifying x2 + 63x + 984 = 0 Reorder the terms: 984 + 63x + x2 = 0 Solving 984 + 63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-984' to each side of the equation. 984 + 63x + -984 + x2 = 0 + -984 Reorder the terms: 984 + -984 + 63x + x2 = 0 + -984 Combine like terms: 984 + -984 = 0 0 + 63x + x2 = 0 + -984 63x + x2 = 0 + -984 Combine like terms: 0 + -984 = -984 63x + x2 = -984 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = -984 + 992.25 Reorder the terms: 992.25 + 63x + x2 = -984 + 992.25 Combine like terms: -984 + 992.25 = 8.25 992.25 + 63x + x2 = 8.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 31.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 31.5 = 2.872281323 Simplifying x + 31.5 = 2.872281323 Reorder the terms: 31.5 + x = 2.872281323 Solving 31.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 2.872281323 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 2.872281323 + -31.5 x = 2.872281323 + -31.5 Combine like terms: 2.872281323 + -31.5 = -28.627718677 x = -28.627718677 Simplifying x = -28.627718677Subproblem 2
x + 31.5 = -2.872281323 Simplifying x + 31.5 = -2.872281323 Reorder the terms: 31.5 + x = -2.872281323 Solving 31.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -2.872281323 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -2.872281323 + -31.5 x = -2.872281323 + -31.5 Combine like terms: -2.872281323 + -31.5 = -34.372281323 x = -34.372281323 Simplifying x = -34.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-28.627718677, -34.372281323}
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