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Simplifying 30 = -0.5x2 + 36x + -132 Reorder the terms: 30 = -132 + 36x + -0.5x2 Solving 30 = -132 + 36x + -0.5x2 Solving for variable 'x'. Combine like terms: 30 + 132 = 162 162 + -36x + 0.5x2 = -132 + 36x + -0.5x2 + 132 + -36x + 0.5x2 Reorder the terms: 162 + -36x + 0.5x2 = -132 + 132 + 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: -132 + 132 = 0 162 + -36x + 0.5x2 = 0 + 36x + -36x + -0.5x2 + 0.5x2 162 + -36x + 0.5x2 = 36x + -36x + -0.5x2 + 0.5x2 Combine like terms: 36x + -36x = 0 162 + -36x + 0.5x2 = 0 + -0.5x2 + 0.5x2 162 + -36x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 162 + -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'. 324 + -72x + x2 = 0 Move the constant term to the right: Add '-324' to each side of the equation. 324 + -72x + -324 + x2 = 0 + -324 Reorder the terms: 324 + -324 + -72x + x2 = 0 + -324 Combine like terms: 324 + -324 = 0 0 + -72x + x2 = 0 + -324 -72x + x2 = 0 + -324 Combine like terms: 0 + -324 = -324 -72x + x2 = -324 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 = -324 + 1296 Reorder the terms: 1296 + -72x + x2 = -324 + 1296 Combine like terms: -324 + 1296 = 972 1296 + -72x + x2 = 972 Factor a perfect square on the left side: (x + -36)(x + -36) = 972 Calculate the square root of the right side: 31.176914536 Break this problem into two subproblems by setting (x + -36) equal to 31.176914536 and -31.176914536.Subproblem 1
x + -36 = 31.176914536 Simplifying x + -36 = 31.176914536 Reorder the terms: -36 + x = 31.176914536 Solving -36 + x = 31.176914536 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 = 31.176914536 + 36 Combine like terms: -36 + 36 = 0 0 + x = 31.176914536 + 36 x = 31.176914536 + 36 Combine like terms: 31.176914536 + 36 = 67.176914536 x = 67.176914536 Simplifying x = 67.176914536Subproblem 2
x + -36 = -31.176914536 Simplifying x + -36 = -31.176914536 Reorder the terms: -36 + x = -31.176914536 Solving -36 + x = -31.176914536 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 = -31.176914536 + 36 Combine like terms: -36 + 36 = 0 0 + x = -31.176914536 + 36 x = -31.176914536 + 36 Combine like terms: -31.176914536 + 36 = 4.823085464 x = 4.823085464 Simplifying x = 4.823085464Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.176914536, 4.823085464}
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