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Simplifying 11x2 + -16x + -60 = 0 Reorder the terms: -60 + -16x + 11x2 = 0 Solving -60 + -16x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -5.454545455 + -1.454545455x + x2 = 0 Move the constant term to the right: Add '5.454545455' to each side of the equation. -5.454545455 + -1.454545455x + 5.454545455 + x2 = 0 + 5.454545455 Reorder the terms: -5.454545455 + 5.454545455 + -1.454545455x + x2 = 0 + 5.454545455 Combine like terms: -5.454545455 + 5.454545455 = 0.000000000 0.000000000 + -1.454545455x + x2 = 0 + 5.454545455 -1.454545455x + x2 = 0 + 5.454545455 Combine like terms: 0 + 5.454545455 = 5.454545455 -1.454545455x + x2 = 5.454545455 The x term is -1.454545455x. Take half its coefficient (-0.7272727275). Square it (0.5289256202) and add it to both sides. Add '0.5289256202' to each side of the equation. -1.454545455x + 0.5289256202 + x2 = 5.454545455 + 0.5289256202 Reorder the terms: 0.5289256202 + -1.454545455x + x2 = 5.454545455 + 0.5289256202 Combine like terms: 5.454545455 + 0.5289256202 = 5.9834710752 0.5289256202 + -1.454545455x + x2 = 5.9834710752 Factor a perfect square on the left side: (x + -0.7272727275)(x + -0.7272727275) = 5.9834710752 Calculate the square root of the right side: 2.446113463 Break this problem into two subproblems by setting (x + -0.7272727275) equal to 2.446113463 and -2.446113463.Subproblem 1
x + -0.7272727275 = 2.446113463 Simplifying x + -0.7272727275 = 2.446113463 Reorder the terms: -0.7272727275 + x = 2.446113463 Solving -0.7272727275 + x = 2.446113463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7272727275' to each side of the equation. -0.7272727275 + 0.7272727275 + x = 2.446113463 + 0.7272727275 Combine like terms: -0.7272727275 + 0.7272727275 = 0.0000000000 0.0000000000 + x = 2.446113463 + 0.7272727275 x = 2.446113463 + 0.7272727275 Combine like terms: 2.446113463 + 0.7272727275 = 3.1733861905 x = 3.1733861905 Simplifying x = 3.1733861905Subproblem 2
x + -0.7272727275 = -2.446113463 Simplifying x + -0.7272727275 = -2.446113463 Reorder the terms: -0.7272727275 + x = -2.446113463 Solving -0.7272727275 + x = -2.446113463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7272727275' to each side of the equation. -0.7272727275 + 0.7272727275 + x = -2.446113463 + 0.7272727275 Combine like terms: -0.7272727275 + 0.7272727275 = 0.0000000000 0.0000000000 + x = -2.446113463 + 0.7272727275 x = -2.446113463 + 0.7272727275 Combine like terms: -2.446113463 + 0.7272727275 = -1.7188407355 x = -1.7188407355 Simplifying x = -1.7188407355Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1733861905, -1.7188407355}
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