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Simplifying 417 = 0.5x2 + 36x + -105 Reorder the terms: 417 = -105 + 36x + 0.5x2 Solving 417 = -105 + 36x + 0.5x2 Solving for variable 'x'. Combine like terms: 417 + 105 = 522 522 + -36x + -0.5x2 = -105 + 36x + 0.5x2 + 105 + -36x + -0.5x2 Reorder the terms: 522 + -36x + -0.5x2 = -105 + 105 + 36x + -36x + 0.5x2 + -0.5x2 Combine like terms: -105 + 105 = 0 522 + -36x + -0.5x2 = 0 + 36x + -36x + 0.5x2 + -0.5x2 522 + -36x + -0.5x2 = 36x + -36x + 0.5x2 + -0.5x2 Combine like terms: 36x + -36x = 0 522 + -36x + -0.5x2 = 0 + 0.5x2 + -0.5x2 522 + -36x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 522 + -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'. -1044 + 72x + x2 = 0 Move the constant term to the right: Add '1044' to each side of the equation. -1044 + 72x + 1044 + x2 = 0 + 1044 Reorder the terms: -1044 + 1044 + 72x + x2 = 0 + 1044 Combine like terms: -1044 + 1044 = 0 0 + 72x + x2 = 0 + 1044 72x + x2 = 0 + 1044 Combine like terms: 0 + 1044 = 1044 72x + x2 = 1044 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 = 1044 + 1296 Reorder the terms: 1296 + 72x + x2 = 1044 + 1296 Combine like terms: 1044 + 1296 = 2340 1296 + 72x + x2 = 2340 Factor a perfect square on the left side: (x + 36)(x + 36) = 2340 Calculate the square root of the right side: 48.37354649 Break this problem into two subproblems by setting (x + 36) equal to 48.37354649 and -48.37354649.Subproblem 1
x + 36 = 48.37354649 Simplifying x + 36 = 48.37354649 Reorder the terms: 36 + x = 48.37354649 Solving 36 + x = 48.37354649 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 = 48.37354649 + -36 Combine like terms: 36 + -36 = 0 0 + x = 48.37354649 + -36 x = 48.37354649 + -36 Combine like terms: 48.37354649 + -36 = 12.37354649 x = 12.37354649 Simplifying x = 12.37354649Subproblem 2
x + 36 = -48.37354649 Simplifying x + 36 = -48.37354649 Reorder the terms: 36 + x = -48.37354649 Solving 36 + x = -48.37354649 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 = -48.37354649 + -36 Combine like terms: 36 + -36 = 0 0 + x = -48.37354649 + -36 x = -48.37354649 + -36 Combine like terms: -48.37354649 + -36 = -84.37354649 x = -84.37354649 Simplifying x = -84.37354649Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.37354649, -84.37354649}
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