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Simplifying 2x2 + -1x = 160 Reorder the terms: -1x + 2x2 = 160 Solving -1x + 2x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + -1x + 2x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -80 + -0.5x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -0.5x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -0.5x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -0.5x + x2 = 0 + 80 -0.5x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -0.5x + x2 = 80 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 80 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 80 + 0.0625 Combine like terms: 80 + 0.0625 = 80.0625 0.0625 + -0.5x + x2 = 80.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 80.0625 Calculate the square root of the right side: 8.947765084 Break this problem into two subproblems by setting (x + -0.25) equal to 8.947765084 and -8.947765084.Subproblem 1
x + -0.25 = 8.947765084 Simplifying x + -0.25 = 8.947765084 Reorder the terms: -0.25 + x = 8.947765084 Solving -0.25 + x = 8.947765084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 8.947765084 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 8.947765084 + 0.25 x = 8.947765084 + 0.25 Combine like terms: 8.947765084 + 0.25 = 9.197765084 x = 9.197765084 Simplifying x = 9.197765084Subproblem 2
x + -0.25 = -8.947765084 Simplifying x + -0.25 = -8.947765084 Reorder the terms: -0.25 + x = -8.947765084 Solving -0.25 + x = -8.947765084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -8.947765084 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -8.947765084 + 0.25 x = -8.947765084 + 0.25 Combine like terms: -8.947765084 + 0.25 = -8.697765084 x = -8.697765084 Simplifying x = -8.697765084Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.197765084, -8.697765084}
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