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Simplifying x2 + 17x = -2 Reorder the terms: 17x + x2 = -2 Solving 17x + x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 17x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 17x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 17x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 17x + x2 = 0 + -2 17x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 17x + x2 = -2 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -2 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -2 + 72.25 Combine like terms: -2 + 72.25 = 70.25 72.25 + 17x + x2 = 70.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + 8.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + 8.5 = 8.381527307 Simplifying x + 8.5 = 8.381527307 Reorder the terms: 8.5 + x = 8.381527307 Solving 8.5 + x = 8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 8.381527307 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.381527307 + -8.5 x = 8.381527307 + -8.5 Combine like terms: 8.381527307 + -8.5 = -0.118472693 x = -0.118472693 Simplifying x = -0.118472693Subproblem 2
x + 8.5 = -8.381527307 Simplifying x + 8.5 = -8.381527307 Reorder the terms: 8.5 + x = -8.381527307 Solving 8.5 + x = -8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -8.381527307 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.381527307 + -8.5 x = -8.381527307 + -8.5 Combine like terms: -8.381527307 + -8.5 = -16.881527307 x = -16.881527307 Simplifying x = -16.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.118472693, -16.881527307}
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