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Simplifying 0.5x2 + 8x + 17 = 0 Reorder the terms: 17 + 8x + 0.5x2 = 0 Solving 17 + 8x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 34 + 16x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + 16x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 16x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 16x + x2 = 0 + -34 16x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 16x + x2 = -34 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -34 + 64 Reorder the terms: 64 + 16x + x2 = -34 + 64 Combine like terms: -34 + 64 = 30 64 + 16x + x2 = 30 Factor a perfect square on the left side: (x + 8)(x + 8) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 8) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 8 = 5.477225575 Simplifying x + 8 = 5.477225575 Reorder the terms: 8 + x = 5.477225575 Solving 8 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 5.477225575 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.477225575 + -8 x = 5.477225575 + -8 Combine like terms: 5.477225575 + -8 = -2.522774425 x = -2.522774425 Simplifying x = -2.522774425Subproblem 2
x + 8 = -5.477225575 Simplifying x + 8 = -5.477225575 Reorder the terms: 8 + x = -5.477225575 Solving 8 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -5.477225575 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.477225575 + -8 x = -5.477225575 + -8 Combine like terms: -5.477225575 + -8 = -13.477225575 x = -13.477225575 Simplifying x = -13.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.522774425, -13.477225575}
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