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Simplifying x2 + 17.54x + -17.3 = 0 Reorder the terms: -17.3 + 17.54x + x2 = 0 Solving -17.3 + 17.54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17.3' to each side of the equation. -17.3 + 17.54x + 17.3 + x2 = 0 + 17.3 Reorder the terms: -17.3 + 17.3 + 17.54x + x2 = 0 + 17.3 Combine like terms: -17.3 + 17.3 = 0.0 0.0 + 17.54x + x2 = 0 + 17.3 17.54x + x2 = 0 + 17.3 Combine like terms: 0 + 17.3 = 17.3 17.54x + x2 = 17.3 The x term is 17.54x. Take half its coefficient (8.77). Square it (76.9129) and add it to both sides. Add '76.9129' to each side of the equation. 17.54x + 76.9129 + x2 = 17.3 + 76.9129 Reorder the terms: 76.9129 + 17.54x + x2 = 17.3 + 76.9129 Combine like terms: 17.3 + 76.9129 = 94.2129 76.9129 + 17.54x + x2 = 94.2129 Factor a perfect square on the left side: (x + 8.77)(x + 8.77) = 94.2129 Calculate the square root of the right side: 9.706332984 Break this problem into two subproblems by setting (x + 8.77) equal to 9.706332984 and -9.706332984.Subproblem 1
x + 8.77 = 9.706332984 Simplifying x + 8.77 = 9.706332984 Reorder the terms: 8.77 + x = 9.706332984 Solving 8.77 + x = 9.706332984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.77' to each side of the equation. 8.77 + -8.77 + x = 9.706332984 + -8.77 Combine like terms: 8.77 + -8.77 = 0.00 0.00 + x = 9.706332984 + -8.77 x = 9.706332984 + -8.77 Combine like terms: 9.706332984 + -8.77 = 0.936332984 x = 0.936332984 Simplifying x = 0.936332984Subproblem 2
x + 8.77 = -9.706332984 Simplifying x + 8.77 = -9.706332984 Reorder the terms: 8.77 + x = -9.706332984 Solving 8.77 + x = -9.706332984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.77' to each side of the equation. 8.77 + -8.77 + x = -9.706332984 + -8.77 Combine like terms: 8.77 + -8.77 = 0.00 0.00 + x = -9.706332984 + -8.77 x = -9.706332984 + -8.77 Combine like terms: -9.706332984 + -8.77 = -18.476332984 x = -18.476332984 Simplifying x = -18.476332984Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.936332984, -18.476332984}
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