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Simplifying 2x2 + -1x + 2 = 180 Reorder the terms: 2 + -1x + 2x2 = 180 Solving 2 + -1x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + -1x + 2x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + -1x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -89 + -0.5x + x2 = 0 Move the constant term to the right: Add '89' to each side of the equation. -89 + -0.5x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + -0.5x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + -0.5x + x2 = 0 + 89 -0.5x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 -0.5x + x2 = 89 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 = 89 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 89 + 0.0625 Combine like terms: 89 + 0.0625 = 89.0625 0.0625 + -0.5x + x2 = 89.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 89.0625 Calculate the square root of the right side: 9.437293044 Break this problem into two subproblems by setting (x + -0.25) equal to 9.437293044 and -9.437293044.Subproblem 1
x + -0.25 = 9.437293044 Simplifying x + -0.25 = 9.437293044 Reorder the terms: -0.25 + x = 9.437293044 Solving -0.25 + x = 9.437293044 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 = 9.437293044 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 9.437293044 + 0.25 x = 9.437293044 + 0.25 Combine like terms: 9.437293044 + 0.25 = 9.687293044 x = 9.687293044 Simplifying x = 9.687293044Subproblem 2
x + -0.25 = -9.437293044 Simplifying x + -0.25 = -9.437293044 Reorder the terms: -0.25 + x = -9.437293044 Solving -0.25 + x = -9.437293044 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 = -9.437293044 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -9.437293044 + 0.25 x = -9.437293044 + 0.25 Combine like terms: -9.437293044 + 0.25 = -9.187293044 x = -9.187293044 Simplifying x = -9.187293044Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.687293044, -9.187293044}
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