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Simplifying x2 + 10.8x + -1296 = 0 Reorder the terms: -1296 + 10.8x + x2 = 0 Solving -1296 + 10.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + 10.8x + 1296 + x2 = 0 + 1296 Reorder the terms: -1296 + 1296 + 10.8x + x2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + 10.8x + x2 = 0 + 1296 10.8x + x2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 10.8x + x2 = 1296 The x term is 10.8x. Take half its coefficient (5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. 10.8x + 29.16 + x2 = 1296 + 29.16 Reorder the terms: 29.16 + 10.8x + x2 = 1296 + 29.16 Combine like terms: 1296 + 29.16 = 1325.16 29.16 + 10.8x + x2 = 1325.16 Factor a perfect square on the left side: (x + 5.4)(x + 5.4) = 1325.16 Calculate the square root of the right side: 36.402747149 Break this problem into two subproblems by setting (x + 5.4) equal to 36.402747149 and -36.402747149.Subproblem 1
x + 5.4 = 36.402747149 Simplifying x + 5.4 = 36.402747149 Reorder the terms: 5.4 + x = 36.402747149 Solving 5.4 + x = 36.402747149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = 36.402747149 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = 36.402747149 + -5.4 x = 36.402747149 + -5.4 Combine like terms: 36.402747149 + -5.4 = 31.002747149 x = 31.002747149 Simplifying x = 31.002747149Subproblem 2
x + 5.4 = -36.402747149 Simplifying x + 5.4 = -36.402747149 Reorder the terms: 5.4 + x = -36.402747149 Solving 5.4 + x = -36.402747149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = -36.402747149 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = -36.402747149 + -5.4 x = -36.402747149 + -5.4 Combine like terms: -36.402747149 + -5.4 = -41.802747149 x = -41.802747149 Simplifying x = -41.802747149Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.002747149, -41.802747149}
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