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Simplifying 270 = 0.5x2 + 36x + -40 Reorder the terms: 270 = -40 + 36x + 0.5x2 Solving 270 = -40 + 36x + 0.5x2 Solving for variable 'x'. Combine like terms: 270 + 40 = 310 310 + -36x + -0.5x2 = -40 + 36x + 0.5x2 + 40 + -36x + -0.5x2 Reorder the terms: 310 + -36x + -0.5x2 = -40 + 40 + 36x + -36x + 0.5x2 + -0.5x2 Combine like terms: -40 + 40 = 0 310 + -36x + -0.5x2 = 0 + 36x + -36x + 0.5x2 + -0.5x2 310 + -36x + -0.5x2 = 36x + -36x + 0.5x2 + -0.5x2 Combine like terms: 36x + -36x = 0 310 + -36x + -0.5x2 = 0 + 0.5x2 + -0.5x2 310 + -36x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 310 + -36x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -620 + 72x + x2 = 0 Move the constant term to the right: Add '620' to each side of the equation. -620 + 72x + 620 + x2 = 0 + 620 Reorder the terms: -620 + 620 + 72x + x2 = 0 + 620 Combine like terms: -620 + 620 = 0 0 + 72x + x2 = 0 + 620 72x + x2 = 0 + 620 Combine like terms: 0 + 620 = 620 72x + x2 = 620 The x term is 72x. Take half its coefficient (36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. 72x + 1296 + x2 = 620 + 1296 Reorder the terms: 1296 + 72x + x2 = 620 + 1296 Combine like terms: 620 + 1296 = 1916 1296 + 72x + x2 = 1916 Factor a perfect square on the left side: (x + 36)(x + 36) = 1916 Calculate the square root of the right side: 43.772137256 Break this problem into two subproblems by setting (x + 36) equal to 43.772137256 and -43.772137256.Subproblem 1
x + 36 = 43.772137256 Simplifying x + 36 = 43.772137256 Reorder the terms: 36 + x = 43.772137256 Solving 36 + x = 43.772137256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = 43.772137256 + -36 Combine like terms: 36 + -36 = 0 0 + x = 43.772137256 + -36 x = 43.772137256 + -36 Combine like terms: 43.772137256 + -36 = 7.772137256 x = 7.772137256 Simplifying x = 7.772137256Subproblem 2
x + 36 = -43.772137256 Simplifying x + 36 = -43.772137256 Reorder the terms: 36 + x = -43.772137256 Solving 36 + x = -43.772137256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x = -43.772137256 + -36 Combine like terms: 36 + -36 = 0 0 + x = -43.772137256 + -36 x = -43.772137256 + -36 Combine like terms: -43.772137256 + -36 = -79.772137256 x = -79.772137256 Simplifying x = -79.772137256Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.772137256, -79.772137256}
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