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Simplifying 2x2 + 3x + -5 = 180 Reorder the terms: -5 + 3x + 2x2 = 180 Solving -5 + 3x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -5 + -180 + 3x + 2x2 = 180 + -180 Combine like terms: -5 + -180 = -185 -185 + 3x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -185 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -92.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '92.5' to each side of the equation. -92.5 + 1.5x + 92.5 + x2 = 0 + 92.5 Reorder the terms: -92.5 + 92.5 + 1.5x + x2 = 0 + 92.5 Combine like terms: -92.5 + 92.5 = 0.0 0.0 + 1.5x + x2 = 0 + 92.5 1.5x + x2 = 0 + 92.5 Combine like terms: 0 + 92.5 = 92.5 1.5x + x2 = 92.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 92.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 92.5 + 0.5625 Combine like terms: 92.5 + 0.5625 = 93.0625 0.5625 + 1.5x + x2 = 93.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 93.0625 Calculate the square root of the right side: 9.646890691 Break this problem into two subproblems by setting (x + 0.75) equal to 9.646890691 and -9.646890691.Subproblem 1
x + 0.75 = 9.646890691 Simplifying x + 0.75 = 9.646890691 Reorder the terms: 0.75 + x = 9.646890691 Solving 0.75 + x = 9.646890691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 9.646890691 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 9.646890691 + -0.75 x = 9.646890691 + -0.75 Combine like terms: 9.646890691 + -0.75 = 8.896890691 x = 8.896890691 Simplifying x = 8.896890691Subproblem 2
x + 0.75 = -9.646890691 Simplifying x + 0.75 = -9.646890691 Reorder the terms: 0.75 + x = -9.646890691 Solving 0.75 + x = -9.646890691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -9.646890691 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -9.646890691 + -0.75 x = -9.646890691 + -0.75 Combine like terms: -9.646890691 + -0.75 = -10.396890691 x = -10.396890691 Simplifying x = -10.396890691Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.896890691, -10.396890691}
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