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Simplifying 414 = -0.5x2 + 36x + -144 Reorder the terms: 414 = -144 + 36x + -0.5x2 Solving 414 = -144 + 36x + -0.5x2 Solving for variable 'x'. Combine like terms: 414 + 144 = 558 558 + -36x + 0.5x2 = -144 + 36x + -0.5x2 + 144 + -36x + 0.5x2 Reorder the terms: 558 + -36x + 0.5x2 = -144 + 144 + 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: -144 + 144 = 0 558 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2 558 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: 36x + -36x = 0 558 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2 558 + -36x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 558 + -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'. 1116 + -72x + x2 = 0 Move the constant term to the right: Add '-1116' to each side of the equation. 1116 + -72x + -1116 + x2 = 0 + -1116 Reorder the terms: 1116 + -1116 + -72x + x2 = 0 + -1116 Combine like terms: 1116 + -1116 = 0 0 + -72x + x2 = 0 + -1116 -72x + x2 = 0 + -1116 Combine like terms: 0 + -1116 = -1116 -72x + x2 = -1116 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 = -1116 + 1296 Reorder the terms: 1296 + -72x + x2 = -1116 + 1296 Combine like terms: -1116 + 1296 = 180 1296 + -72x + x2 = 180 Factor a perfect square on the left side: (x + -36)(x + -36) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -36) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -36 = 13.416407865 Simplifying x + -36 = 13.416407865 Reorder the terms: -36 + x = 13.416407865 Solving -36 + x = 13.416407865 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 = 13.416407865 + 36 Combine like terms: -36 + 36 = 0 0 + x = 13.416407865 + 36 x = 13.416407865 + 36 Combine like terms: 13.416407865 + 36 = 49.416407865 x = 49.416407865 Simplifying x = 49.416407865Subproblem 2
x + -36 = -13.416407865 Simplifying x + -36 = -13.416407865 Reorder the terms: -36 + x = -13.416407865 Solving -36 + x = -13.416407865 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 = -13.416407865 + 36 Combine like terms: -36 + 36 = 0 0 + x = -13.416407865 + 36 x = -13.416407865 + 36 Combine like terms: -13.416407865 + 36 = 22.583592135 x = 22.583592135 Simplifying x = 22.583592135Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.416407865, 22.583592135}
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