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Simplifying x2 + 17x = -49 Reorder the terms: 17x + x2 = -49 Solving 17x + x2 = -49 Solving for variable 'x'. Reorder the terms: 49 + 17x + x2 = -49 + 49 Combine like terms: -49 + 49 = 0 49 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + 17x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + 17x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 17x + x2 = 0 + -49 17x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 17x + x2 = -49 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 = -49 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -49 + 72.25 Combine like terms: -49 + 72.25 = 23.25 72.25 + 17x + x2 = 23.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + 8.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + 8.5 = 4.82182538 Simplifying x + 8.5 = 4.82182538 Reorder the terms: 8.5 + x = 4.82182538 Solving 8.5 + x = 4.82182538 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 = 4.82182538 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 4.82182538 + -8.5 x = 4.82182538 + -8.5 Combine like terms: 4.82182538 + -8.5 = -3.67817462 x = -3.67817462 Simplifying x = -3.67817462Subproblem 2
x + 8.5 = -4.82182538 Simplifying x + 8.5 = -4.82182538 Reorder the terms: 8.5 + x = -4.82182538 Solving 8.5 + x = -4.82182538 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 = -4.82182538 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -4.82182538 + -8.5 x = -4.82182538 + -8.5 Combine like terms: -4.82182538 + -8.5 = -13.32182538 x = -13.32182538 Simplifying x = -13.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.67817462, -13.32182538}
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