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Simplifying 0 = -0.5x2 + 36x + -144 Reorder the terms: 0 = -144 + 36x + -0.5x2 Solving 0 = -144 + 36x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 144 = 144 144 + -36x + 0.5x2 = -144 + 36x + -0.5x2 + 144 + -36x + 0.5x2 Reorder the terms: 144 + -36x + 0.5x2 = -144 + 144 + 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: -144 + 144 = 0 144 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2 144 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: 36x + -36x = 0 144 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2 144 + -36x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 144 + -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'. 288 + -72x + x2 = 0 Move the constant term to the right: Add '-288' to each side of the equation. 288 + -72x + -288 + x2 = 0 + -288 Reorder the terms: 288 + -288 + -72x + x2 = 0 + -288 Combine like terms: 288 + -288 = 0 0 + -72x + x2 = 0 + -288 -72x + x2 = 0 + -288 Combine like terms: 0 + -288 = -288 -72x + x2 = -288 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 = -288 + 1296 Reorder the terms: 1296 + -72x + x2 = -288 + 1296 Combine like terms: -288 + 1296 = 1008 1296 + -72x + x2 = 1008 Factor a perfect square on the left side: (x + -36)(x + -36) = 1008 Calculate the square root of the right side: 31.749015733 Break this problem into two subproblems by setting (x + -36) equal to 31.749015733 and -31.749015733.Subproblem 1
x + -36 = 31.749015733 Simplifying x + -36 = 31.749015733 Reorder the terms: -36 + x = 31.749015733 Solving -36 + x = 31.749015733 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 = 31.749015733 + 36 Combine like terms: -36 + 36 = 0 0 + x = 31.749015733 + 36 x = 31.749015733 + 36 Combine like terms: 31.749015733 + 36 = 67.749015733 x = 67.749015733 Simplifying x = 67.749015733Subproblem 2
x + -36 = -31.749015733 Simplifying x + -36 = -31.749015733 Reorder the terms: -36 + x = -31.749015733 Solving -36 + x = -31.749015733 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 = -31.749015733 + 36 Combine like terms: -36 + 36 = 0 0 + x = -31.749015733 + 36 x = -31.749015733 + 36 Combine like terms: -31.749015733 + 36 = 4.250984267 x = 4.250984267 Simplifying x = 4.250984267Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.749015733, 4.250984267}
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