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Simplifying -0.5x2 + 36x + -206 = 0 Reorder the terms: -206 + 36x + -0.5x2 = 0 Solving -206 + 36x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 412 + -72x + x2 = 0 Move the constant term to the right: Add '-412' to each side of the equation. 412 + -72x + -412 + x2 = 0 + -412 Reorder the terms: 412 + -412 + -72x + x2 = 0 + -412 Combine like terms: 412 + -412 = 0 0 + -72x + x2 = 0 + -412 -72x + x2 = 0 + -412 Combine like terms: 0 + -412 = -412 -72x + x2 = -412 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 = -412 + 1296 Reorder the terms: 1296 + -72x + x2 = -412 + 1296 Combine like terms: -412 + 1296 = 884 1296 + -72x + x2 = 884 Factor a perfect square on the left side: (x + -36)(x + -36) = 884 Calculate the square root of the right side: 29.732137495 Break this problem into two subproblems by setting (x + -36) equal to 29.732137495 and -29.732137495.Subproblem 1
x + -36 = 29.732137495 Simplifying x + -36 = 29.732137495 Reorder the terms: -36 + x = 29.732137495 Solving -36 + x = 29.732137495 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 = 29.732137495 + 36 Combine like terms: -36 + 36 = 0 0 + x = 29.732137495 + 36 x = 29.732137495 + 36 Combine like terms: 29.732137495 + 36 = 65.732137495 x = 65.732137495 Simplifying x = 65.732137495Subproblem 2
x + -36 = -29.732137495 Simplifying x + -36 = -29.732137495 Reorder the terms: -36 + x = -29.732137495 Solving -36 + x = -29.732137495 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 = -29.732137495 + 36 Combine like terms: -36 + 36 = 0 0 + x = -29.732137495 + 36 x = -29.732137495 + 36 Combine like terms: -29.732137495 + 36 = 6.267862505 x = 6.267862505 Simplifying x = 6.267862505Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.732137495, 6.267862505}
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