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Simplifying 5x2 + -72x + -216 = 0 Reorder the terms: -216 + -72x + 5x2 = 0 Solving -216 + -72x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -43.2 + -14.4x + x2 = 0 Move the constant term to the right: Add '43.2' to each side of the equation. -43.2 + -14.4x + 43.2 + x2 = 0 + 43.2 Reorder the terms: -43.2 + 43.2 + -14.4x + x2 = 0 + 43.2 Combine like terms: -43.2 + 43.2 = 0.0 0.0 + -14.4x + x2 = 0 + 43.2 -14.4x + x2 = 0 + 43.2 Combine like terms: 0 + 43.2 = 43.2 -14.4x + x2 = 43.2 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = 43.2 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = 43.2 + 51.84 Combine like terms: 43.2 + 51.84 = 95.04 51.84 + -14.4x + x2 = 95.04 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 95.04 Calculate the square root of the right side: 9.748846086 Break this problem into two subproblems by setting (x + -7.2) equal to 9.748846086 and -9.748846086.Subproblem 1
x + -7.2 = 9.748846086 Simplifying x + -7.2 = 9.748846086 Reorder the terms: -7.2 + x = 9.748846086 Solving -7.2 + x = 9.748846086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = 9.748846086 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 9.748846086 + 7.2 x = 9.748846086 + 7.2 Combine like terms: 9.748846086 + 7.2 = 16.948846086 x = 16.948846086 Simplifying x = 16.948846086Subproblem 2
x + -7.2 = -9.748846086 Simplifying x + -7.2 = -9.748846086 Reorder the terms: -7.2 + x = -9.748846086 Solving -7.2 + x = -9.748846086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = -9.748846086 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -9.748846086 + 7.2 x = -9.748846086 + 7.2 Combine like terms: -9.748846086 + 7.2 = -2.548846086 x = -2.548846086 Simplifying x = -2.548846086Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.948846086, -2.548846086}
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