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Simplifying 0.5x2 + 8x + 2 = 0 Reorder the terms: 2 + 8x + 0.5x2 = 0 Solving 2 + 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'. 4 + 16x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 16x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 16x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 16x + x2 = 0 + -4 16x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 16x + x2 = -4 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 = -4 + 64 Reorder the terms: 64 + 16x + x2 = -4 + 64 Combine like terms: -4 + 64 = 60 64 + 16x + x2 = 60 Factor a perfect square on the left side: (x + 8)(x + 8) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 8) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 8 = 7.745966692 Simplifying x + 8 = 7.745966692 Reorder the terms: 8 + x = 7.745966692 Solving 8 + x = 7.745966692 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 = 7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.745966692 + -8 x = 7.745966692 + -8 Combine like terms: 7.745966692 + -8 = -0.254033308 x = -0.254033308 Simplifying x = -0.254033308Subproblem 2
x + 8 = -7.745966692 Simplifying x + 8 = -7.745966692 Reorder the terms: 8 + x = -7.745966692 Solving 8 + x = -7.745966692 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 = -7.745966692 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.745966692 + -8 x = -7.745966692 + -8 Combine like terms: -7.745966692 + -8 = -15.745966692 x = -15.745966692 Simplifying x = -15.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.254033308, -15.745966692}
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