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Simplifying 0.2x2 + 3.2x + -5 = 0 Reorder the terms: -5 + 3.2x + 0.2x2 = 0 Solving -5 + 3.2x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -25 + 16x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 16x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 16x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 16x + x2 = 0 + 25 16x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 16x + x2 = 25 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 = 25 + 64 Reorder the terms: 64 + 16x + x2 = 25 + 64 Combine like terms: 25 + 64 = 89 64 + 16x + x2 = 89 Factor a perfect square on the left side: (x + 8)(x + 8) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 8) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 8 = 9.433981132 Simplifying x + 8 = 9.433981132 Reorder the terms: 8 + x = 9.433981132 Solving 8 + x = 9.433981132 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 = 9.433981132 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.433981132 + -8 x = 9.433981132 + -8 Combine like terms: 9.433981132 + -8 = 1.433981132 x = 1.433981132 Simplifying x = 1.433981132Subproblem 2
x + 8 = -9.433981132 Simplifying x + 8 = -9.433981132 Reorder the terms: 8 + x = -9.433981132 Solving 8 + x = -9.433981132 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 = -9.433981132 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.433981132 + -8 x = -9.433981132 + -8 Combine like terms: -9.433981132 + -8 = -17.433981132 x = -17.433981132 Simplifying x = -17.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.433981132, -17.433981132}
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